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V 


AN ELEMENTARY TREATISE 


ON 


HEAT, 


BY 


WILLIAM GARNETT, M.A. Ah.3.c./. j 

. '» . 

(LATE WHITWORTH SCHOLAR), 

FORMERLY FELLOW OF ST JOHN’S COLLEGE, AND DEMONSTRATOR OF 
EXPERIMENTAL PHYSICS IN THE UNIVERSITY OF CAMBRIDGE ; 
fo4*i*AL'l PROFESSOR OF MATHEMATICS, PHYSICS AND MECHANICS 
IN UNIVERSITY COLLEGE, NOTTINGHAM, AND 
EXAMINER IN NATURAL PHILOSOPHY IN 
THE UNIVERSITY OF LONDON. 






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, THIRD EDITION , REVISED AND ENLARGED. 



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CAMBRIDGE: 
DEIGHTON, BELL AND CO. 
LONDON: GEORGE BELL AND SONS. 

1884 



Cambrtoge: 

PRINTED BY C. J. CLAY, M.A. AND SON, 
AT THE UNIVERSITY PRESS. 




Gift 

<J.D. Thorps on 

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CONTENTS. 


CHAPTER I. 

PAGE 

Temperature and its Measurement-.1 


CHAPTER II. 

Heat as a quantity. Calorimetry.21 

CHAPTER III. 

Sources of Heat.37 

CHAPTER IV. 

Effects of Heat upon Matter.48 


CHAPTER Y. 

Gases and the Gaseous Laws.71 


CHAPTER VI. 

Change of State.87 


CHAPTER VII. 

Effects of Heat upon the Mechanical, Magnetic and Electrical 
Properties of Matter. 


123 






IV 


CONTENTS. 


CHAPTER VIII. 

PAGK 

The Transmission of Heat.131 

CHAPTER IX. 

Radiant Energy.117 

CHAPTER X. 

Meteorology.171 

CHAPTER XI. 

Conservation and Dissipation of Energy and the Mechanical 

Equivalent of Heat.177 

CHAPTER XII. 

Indicator Diagrams.204 

Examples (from University and other Examination Papers) . 221 

Index.239 







CHAPTER I. 


ON TEMPERATURE AND ITS MEASUREMENT. THE MERCURIAL 
THERMOMETER. MAXIMUM AND MINIMUM THERMOME¬ 
TERS. 

1. If we place a poker in a fire, and after some time 
remove it, it feels hot The physical' cause of this sensation 
is called heat A piece of iron which has been exposed to 
the air in Britain will generally feel cold. 

If we hold for some time in the right hand a piece 
of iron which feels hot, and then grasp the right hand with 
the left, the left hand will experience a sensation of heat, or 
the right hand will feel hot to the left, and at the same time 
the left hand will feel cold to the right. The same will be 
true if we hold for some time in the right hand any other 
body which feels hot. The fact that the right hand feels hot 
to the left after holding the hot iron, while it may have felt 
neither hot nor cold before, proves that the hand has re¬ 
ceived heat from the iron. We therefore infer that when 
a body feels hot to the hand it imparts heat to the hand 
while touching it. It then follows that, because the right 
hand feels hot to the left hand, heat must pass from the 
right hand to the left. But the left hand feels cold to the 
right hand and associating this sensation with what we have 
just proved, viz., that heat passes from the right hand to the 
left, we infer that a body feels cold to the hand when heat 
passes from the hand to the body. We may arrive at the 
same conclusion by holding in the right hand a piece of very 
cold iron, after which the right hand will feel cold to the 
left, and the left hand warm to the right. Now, the fact 
that the left hand feels warm to the right, shews that heat 

1 


G. 


2 


TEMPERATURE. 


passes from it to the right hand, and we infer that this also 
is the reason why the right hand feels cold to the left. Also 
the fact that the right hand has been made to feel cold 
to the left by its contact with the iron, shews that heat 
must have left the hand and entered the iron, which ac¬ 
counts for the latter feeling cold to the hand. 

2. We thus see that a body feels hot to the hand when 
heat passes from the body to the hand, and cold when it 
passes in the opposite direction. The sensations of heat and 
cold are therefore essentially relative. This may be further 
illustrated thus:— 

Place the right hand in a mixture of ice and salt and 
the left hand in hot water, then place both in cold water; 
the cold water will feel warm to the right hand and cold to 
the left, shewing that the sensation of heat or cold depends 
on the condition of the hand relative to the hot or cold body, 
and not simply on the state of the body itself. The water 
in a bath sometimes feels warm to the hands and cold to the 
feet. 

3. The quality of a body , in virtue of which it seems hot 
or cold , is called its temperature. If a body feel hot to the 
hand, it is said to be at a higher temperature, and if it feel 
cold, at a lower temperature, than the hand. Now we have 
seen that a body feels hot or cold according as heat passes 
from it to the hand, or from the hand to it. The direction 
of the flow of heat then, in this case, determines whether the 
body or the hand is at the higher temperature; and apply¬ 
ing the same criterion in all cases to determine whether of 
two bodies is the hotter, we may define temperature thus :— 

Def. The temperature of a body is its thermal condition 
with reference to its power of communicating heat to, or of 
receiving heat from , other bodies; the body A being said to 
have a higher temperature than B ifB gain heat from A when 
they are placed in contact. 

Hence , if when two bodies are placed in contact neither of 
them gain heat at the expense of the other , the two bodies are 
said to be at the same temperature. 

4. When two bodies have the same temperature, they 
are said to be in thermal equilibrium with each other. 


TEMPERATURE. 


3 


Now it is found experimentally that if two bodies A and 
O are each in thermal equilibrium with a third body B , then 
if A and C be placed in contact, they will be in thermal 
equilibrium with each other, provided no chemical action 
take place between them. Hence we infer that, bodies 
which are in thermal equilibrium with the same body , are in 
thermal equilibrium with each other; and our definition is 
consistent with itself when it directs us to assign to them all 
the same temperature, viz., that of the body with which 
they are all in thermal equilibrium. It is on this principle 
that the employment of thermometers depends. If two bodies 
act chemically upon one another they may be put into thermal 
communication with each other by means of a diaphragm 
impervious to either body, but pervious to heat. If no heat 
be lost or gained by either from the other the bodies are in 
thermal equilibrium, but it will be seen that unless radiation 
can take place between them all we can say respecting them 
is that they are each in thermal equilibrium with the dia¬ 
phragm, and this is no more than saying that they are in 
thermal equilibrium with a third body. 

5. If we touch in succession several bodies all of which 
feel hot, some will feel hotter than others; and similarly, if 
we touch several bodies all of which feel cold, we shall expe¬ 
rience sensations of different degrees of coldness. Now if all 
the bodies are formed of the same material, and in the same 
mechanical condition, we are justified in assuming that, of 
two hot bodies, that is at the higher temperature which feels 
the hotter, and similarly for two cold bodies. But if the 
bodies be of different materials we are no longer justified in 
making this assumption, and for this reason; viz., that the 
power of a hot body to produce the sensation of heat does 
not depend entirely on its thermal condition with reference to 
its power of communicating heat to other bodies (that is, on 
its temperature), but depends also on the rate at which it can 
transmit heat through its substance, and this is different for 
different materials. Thus a piece of iron and a hollow piece 
of wood may both feel hot, and the iron feel much hotter 
than the wood; yet if the iron be placed in the hollow of 
the wood for some time, it may then feel hotter than before, 
thus shewing that heat has passed from the wood to the 

1—2 


4 


MEASURE OF TEMPERATURE. 


iron, and that the iron was therefore originally at a tempera¬ 
ture lower than that of the wood. Again, if a piece of iron 
and a piece of wood be in contact for a long while in a hot 
place, the iron will feel much the hotter though it is in 
thermal equilibrium with the wood, and therefore at the 
same temperature as the latter. This is due to the differ¬ 
ence in the conducting powers for heat of iron and wood, and 
will be discussed in a subsequent chapter. In fact, the in¬ 
tensity of the sensation of heat depends on the rate at which 
heat enters the skin, and not simply on the temperature of 
the body touched. 

6. In order, then, to determine whether of two bodies 
A and B is the hotter, we ought to place them in contact, 
and determine in which direction the heat passes; but as this 
is frequently a very difficult, or impossible, operation, recourse 
must be had to some more convenient method. This is ge¬ 
nerally accomplished by taking a third body (7, very small 
compared with A or B } and called a thermometer. This is 
placed in contact with A till it is in thermal equilibrium 
with it, and therefore at the same temperature; and sub¬ 
sequently in contact with B , till it is again in thermal equi¬ 
librium, and therefore at the temperature of B ; and it is 
ascertained whether the temperature of C is higher when in 
equilibrium with A or with B by observation of some pro¬ 
perty of the body G, which changes with its temperature, as, 
for example, its volume. 

If the body C be in precisely the same thermal condition 
both when it is in thermal equilibrium with A and when in 
thermal equilibrium with B, it follows from Art. 4 that A 
and B are at the same temperature. Hence, a thermometer 
will enable us to determine whether a number of bodies are 
at the same temperature or not, and if not, to arrange them 
in the order of their respective temperatures. 

Though the changes in volume of the thermometric 
substance are generally taken to indicate the variations of 
temperature which it experiences we may avail ourselves 
of any other property of the thermometric substance which 
changes with temperature and which can be readily observed. 
Thus in tempering steel the colour exhibited by the thin 
film of oxide on its surface serves to indicate the temperature. 


MEASURE OF TEMPERATURE. 


5 


Sometimes the electrical resistance of a platinum wire, which 
increases with the temperature, is employed to indicate the 
temperature to which the wire is exposed; or the thermo¬ 
electric current produced by a pair of dissimilar metals 
is employed to indicate the difference of temperature of 
the junctions of the metals. The 'pitch of the note of an 
organ pipe will indicate the temperature of the air, and as 
nearly all the physical properties of bodies change with the 
temperature almost any property may be made available for 
thermometric purposes. 

7. All bodies, with very few exceptions, among which 
may be mentioned iodide of silver, stretched caoutchouc (in 
the direction of the tension), water at or near the freezing 
point and some alloys, expand when heated, and contract 
again on cooling, so that, other things being the same, their 
volumes increase as the temperature rises, and return to their 
original values when the bodies regain their original tempera¬ 
ture ; though glass presents a curious exception to the last 
statement as its volume does not return to its original value 
after expansion until a long time after the original tempera¬ 
ture has been restored. Suppose it possible to measure 
accurately the volume of a given small quantity of some 
substance, as, for instance, mercury. Then if the mercury 
be placed in contact with each of any number of bodies 
in succession, till it is in thermal equilibrium with it, and its 
volume be measured in each case, we can arrange the series 
of bodies in order of temperature. 

8. Suppose K, L, and M to be three bodies of which 
K is the coldest and M the hottest. Then, although we can 
arrange the bodies in order of temperature by means of the 
small quantity of mercury, or other substance, whose volume 
we measure, yet we are not at present in a position to tell 
whether the difference between the temperatures of K and 
L is greater, equal to, or less than, the difference between 
the temperatures of L and M\ in fact we have as yet no 
graduated scale of temperature. Now, if our thermometer 
consist of a given mass of mercury, we may, if we please, 
define equal increments of temperature to be such as pro¬ 
duce equal increments in the volume of the mercury, and it 
will then follow directly from the definition that the differ- 


6 


MEASURE OF TEMPERATURE. 


ence between the temperatures of two bodies is proportional 
to the difference in the volume of a given mass of mercury 
when in thermal equilibrium with the first and second body 
respectively. We are thus enabled to form an arbitrary 
scale of temperature which will depend upon the properties 
of the particular substance (in this case mercury) which 
forms our thermometer. As, however, the mercurial ther¬ 
mometer is used much more extensively than any other, 
before alluding to other scales of temperature we shall de¬ 
scribe the construction and mode of graduation of the ordi¬ 
nary mercurial thermometer. 

The problem of comparing differences of temperature in 
different parts of the scale, or of determining equal intervals 
of temperature, is comparable in difficulty with the corre¬ 
sponding problem in time. We meet with no such difficulty ~ 
in the measurement of lengths because the lengths which are 
to be compared may be superposed, or a third body of constant 
length may be superposed on each in succession. It is 
obvious, however, that an interval of time of to-day cannot 
thus be compared with an interval to-morrow, for having once 
elapsed it is gone for ever and some other method of com¬ 
paring intervals of time must be resorted to. The First Law 
of Motion indicates the criterion of equality in intervals 
of time. The principles of Thermodynamics teach us how to 
determine the equality of intervals of temperature but until 
we have studied the action of heat engines we must be 
content with a scale of temperature derived from the 
properties of some particular substance or group of sub¬ 
stances. 

9. If we wish to detect and measure very small incre¬ 
ments in the volume of a substance, it is obviously most 
convenient to employ, when possible, a fluid as the substance 
whose volume is to be changed, for we can then avail our¬ 
selves of a large volume of fluid contained in a suitable reser¬ 
voir (e. g. the bulb of the thermometer), while we can cause 
the free surface to be contained in a tube of very small bore, 
and thus an extremely small increase in the volume of the 
fluid will be accompanied by a considerable movement of the 
surface in the tube. In this case it is plain that the change 
of volume observed is only the difference between the change 


THE MERCCJIHAL THERMOMETER. 


7 


of volume of the fluid and of the envelope in which it is con¬ 
tained; but this is no serious inconvenience, since fluids can 
be found which expand very much more than glass, of which 
the envelope is usually made; and even if we employed 
solid bars, we should have to take care that our measuring 
instruments did not themselves expand, or we should obtain 
no better result. 


v 


6 


10. To construct a mercurial thermometer a Fig - 
glass tube of very fine bore is taken, and a small 
bulb is blown at one end, while a cup is formed 
at the other extremity as shewn in Fig. 1. In 
this cup is placed a small quantity of mercury, 
and the bulb is then heated over a flame. The 
air in the bulb expands when heated, and a con¬ 
siderable portion of it escapes by bubbling up 
through the mercury in the cup. The bulb is 
then allowed to cool, when the pressure of the air 
within it diminishes (as explained in Chapter IV.), 
and the pressure of the external air drives some 
of the mercury in the cup down the tube and into the bulb. 
If it be desired to take great care in the construction of 
the thermometer, this process is repeated until the bulb 
and a portion of the tube are filled with mercury when at the 
ordinary temperature; but in general a more expeditious 
process is adopted. A small portion of mercury having 
entered the bulb, as described above, the latter is heated 
until the mercury boils, when the heavy mercury vapour 
drives out the lighter air at the top of the tube, and, when 
the whole of the air has been expelled, the bulb and tube 
are filled with mercury vapour (except the space occupied 
by the liquid mercury remaining in the bulb). The instru¬ 
ment is then allowed to cool, and as the mercury vapour 
condenses, the mercury in the cup is forced into the tube 
by the pressure of the external air, and, except for a very 
small quantity of air which may have been left behind, 
the bulb and tube are completely filled with liquid mercury. 
The instrument is then heated to a temperature somewhat 
higher than the highest for which it is intended to be suo- 
sequently used, when the mercury expands so as to com¬ 
pletely fill the tube, and drive out any residue of air which 



8 


DETERMINATION OF THE FREEZING POINT. 


may have been left above it. The top of the tube is then 
sealed with the blowpipe while the mercury remains hot. 
The instrument should be kept for some months after the 
bulb has been blown before it is graduated, because glass 
after being highly heated does not acquire its permanent 
volume for some time, and this is the reason why, in the 
filling of the best thermometers to be used for moderate 
temperatures only, the mercury is not boiled, but the air is 
driven from the bulb by heating it slightly many times in 
succession. (See Art. 7.) 

The external diameter of the tube of a thermometer 
is generally very great compared with the diameter of the 
bore. Moreover, it is of importance for many purposes that 
the bulb should be constructed of very thin glass. In most 
well-made thermometers the bulb is elongated so as to 
be almost cylindrical, while its external diameter is fre¬ 
quently not greater than that of the tube. The section 
of the bore of the tube is often flattened instead of circular 
so that the mercury may expose a broad surface to the 
front of the thermometer though its sectional area remains 
very small. 

11. It remains to graduate the thermometer. It is 
found that under ordinary atmospheric pressure pure ice 
always melts at the same temperature, which is called the 
freezing point, and also that the temperature of the steam 
above the surface of boiling water depends only on the 
barometric pressure to which it is subjected. A pressure of 
29 905* inches of mercury at the freezing point in the 
latitude of London and at the level of the sea is generally 
taken as the standard pressure, and the temperature of the 
steam above the surface of water boiling under this pressure 

* The pressure of the standard atmosphere is generally taken to be equal 
to that of 760 millimetres or 29*9215...inches of mercury at 0°C. at the sea- 
level in latitude 45°. On account of the variation of gravity with the 
latitude this is equivalent to the pressure exerted by 29'905 inches of 
mercury at the sea-level in the latitude of London, or by 29*898 inches 
of mercury in the latitude of Manchester. In order to avoid ambiguity 
arising from the variation of gravity, it has been proposed to adopt as 
the standard pressure a pressure of a megadyne per square centimetre. 
This is equivalent to 74*964 centimetres or 29*514 inches of mercury at 0°C. 
at the sea-level in the latitude of London. This would, however, necessitate 
a reconstruction of our thermometric scales, since the temperature of steam 
above water boiling under this pressure is only about 93*63° C. 


DETERMINATION OF THE BOILING POINT. 9 

is always the same, and is called the boiling point. If the 
height of the barometer differ from this standard height, in 
graduating the thermometer a correction has to be made in 
consequence. (The correction amounts to about T4° F.* for 
one inch of mercury.) 

In order to graduate the instrument it is first placed 
in melting ice, and a mark made on the tube at the height 
at which the surface of the mercury stands. This mark 
corresponds to the freezing point, and should always be 
determined before the boiling point, because when it has 
been heated to the latter temperature, the glass does not .at 
once contract to its proper volume, and, if the freezing point 
were determined immediately after the boiling point, the 
mark would after some time be found to be too far down 
the tube. In determining the freezing point the thermo¬ 
meter should be immersed so far in the ice that the surface 
of the mercury is only just visible above it, in order that 
the whole of the mercury may have the temperature of 
the ice. In determining the freezing point it is not generally 
necessary to observe the height of the barometer, for the 

1 0 

melting point of ice is lowered by only F. for an increase 

of pressure amounting to a whole atmosphere. 

12. In order to determine the boiling point, the instru¬ 
ment shewn in Fig. 2 and called a hypsometer 
is employed. This instrument consists of a 
vessel A, containing water, the upper portion 
of which is a tube open at the top. Over this 
tube is placed the wider tube BO, which is 
closed at B by a perforated cork through which 
the stem of the thermometer T passes. C is a 
small tube for the exit of the steam, sloping 
downwards in order to allow the ready escape 
of condensed water. I) is a small bent 
tube containing water, which is sometimes at¬ 
tached to the instrument to indicate if the 
pressure of the steam within exceed that of the 
external air. When the water in A is made 
to boil, the thermometer soon becomes sur¬ 
rounded by an atmosphere of steam, which is 

* For description of Fahrenheit’s scale see Art. 15. 


Fig. 2. 








10 


DETERMINATION OF THE BOILING POINT. 


itself surrounded by a steam-jacket, on account of the steam 
having to pass down between the tubes before escaping at 
G y and is thereby prevented from cooling. The thermometer 
is pushed through the cork at B till the surface of the mer¬ 
cury is only just visible above it, in order that the whole of 
the mercury may be exposed to the same temperature. The 
stem is then scratched at the level of the surface of the mer¬ 
cury (the height of the barometer being observed at the same 
time, in order to make any necessary correction for the pres¬ 
sure not being the standard pressure of 29 905 inches of mer¬ 
cury). The mark so placed upon the tube is called the boil¬ 
ing point. 

13. It is important that the thermometer should be im¬ 
mersed in the steam and not in the water, for the tempera¬ 
ture at which the water will boil depends on a great many 
conditions. For example, the material of which the vessel is 
composed affects the boiling point, and water will boil in a 
metallic vessel at a lower temperature than in a vessel made 
of glass. Again, saline impurities dissolved in the water will 
cause the boiling point to be raised, but the temperature of 
the steam above the surface of the water depends only on the 
pressure. 

If a quantity of common salt be dissolved in the water 
the temperature of the solution may be raised about 16° F. 
above the boiling point, but the temperature of the steam 
will be the boiling point due to the existing pressure. If two 
thermometers be immersed in the steam above the solution 
of salt, one of which has its bulb naked and clean while the 
other has a piece of cotton cord, which has been dipped in a 
strong solution of calcic chloride, twisted round the bulb, the 
naked thermometer will indicate 212° F. while the other may 
denote a temperature of 227° F. or even higher. At the same 
time a third thermometer immersed in the solution will read 
228° F. This experiment shews that care should be taken to 
see that the bulb of the thermometer is clean when immersed 
in the steam. 

14. It is very important that when the fixed points are 
marked upon a thermometer tube the tube should be in the 
same position relative to the vertical as that in which it is to 


SCALES OF TEMPERATURE. 


11 


be subsequently used. For if a thermometer be observed in 
a horizontal position, and be then turned into the vertical 
position, the reading will be lowered in consequence of the 
increased pressure in the bulb, and the effect will be greater 
the longer the column of mercury and the thinner the walls 
of the bulb. 

As the air has no access to the interior of a thermometer 
it follows that the reading of a thermometer will depend to 
some extent on the barometric pressure, for the pressure of 
the air will compress the bulb of the thermometer diminish¬ 
ing its volume by an amount depending on that pressure. 
This can be rendered very apparent by placing a thermometer 
in the receiver of an air pump and exhausting the air when 
the thermometer will continue depressed after sufficient time 
has been allowed for the interior of the receiver to regain its 
original temperature, the depression being due to the ex¬ 
pansion of the glass under the diminished pressure of the air. 
When self-registering mercurial thermometers are employed 
for determining the temperature at considerable depths in 
the sea great care must be taken to protect the bulbs from 
the great pressure to which they would otherwise be exposed. 

15. It remains now to subdivide the stem of the ther¬ 
mometer between the freezing and boiling points into de¬ 
grees, and to mark off degrees above the higher and below 
the lower of these temperatures. There are three different 
modes of doing this in general use in different parts of 
Europe, in other words, there are three distinct scales of 
temperature. In Fahrenheit’s scale, which is chiefly adopted 
in England, the freezing point is marked 32° and the 
boiling point 212°. The tube between these points is then 
divided into 180 equal portions, and divisions equal to these 
marked off above 212° and below 32°. In the scale of 
Celsius, better known as the Centigrade scale, the freezing 
point is marked 0°, and the boiling point 100°, the tube 
between these points being divided into 100 equal parts 
and equal divisions marked off along the rest of the tube. 
This scale of temperature is now almost universally adopted 
by scientific men. The third scale of temperature, viz. that 
of Reaumur, is in very general use in ordinary life on the 
Continent. In it, as in the centigrade scale, the freezing 


12 


CALIBRATION OF THE TUBE. 


point is marked 0°, but the boiling point is marked 80°. 
This scale, like that of Fahrenheit, has little to recommend 
it in preference to the centigrade, except its general use in 
some localities. 

16. We shall now suppose that we are graduating a 
centigrade thermometer, and that the freezing and boiling 
points have- been marked upon its stem as described above. 
If the thermometer is not required for very accurate mea¬ 
surements the remainder of the work is very simple. The 
length of tube between the freezing and boiling points is 
divided into 100 equal parts, and these are marked off upon 
the tube, or on a box-wood or metal scale attached to it, by 
means of a dividing engine or otherwise, equal divisions 
being then carried on throughout the remainder of the tube. 
Each division thus' marked is called a degree, and those de¬ 
grees which lie below the 
are marked negative. 

17. Now it is obvious that if there be any inequalities 
in the bore of the thermometer tube in different parts, 
equal lengths of the tube will not always correspond to 
equal increments in the volume of the mercury relative to 
that of the glass. The above mode of graduation is therefore 
not sufficiently exact for accurate instruments. In order to 
remove this cause of error, a small pellet of mercury, of a 
convenient length, is detached from the rest of the column, 
and by inclining and gently tapping the tube, is made to 
occupy different positions within it. The length of the 
pellet in each position is carefully measured, and, since 
its volume is constant, it follows that, if the length of a 
degree at any part of the tube is made proportional to the 
length of the pellet when occupying this position, each 
degree will correspond to the same increment of the apparent 
volume of the mercury in the glass. This process is called cali¬ 
brating the tube. The division of the tube is then conducted 
on this principle, and it is obvious that care and calculation 
are required in effecting it. A small pellet of almost any 
desired length can generally be removed from the rest of the 
column by tapping it so as to remove a long pellet, warming 
it, re-uniting the pellet to the column, cooling it and again 
tapping the tube. A pellet will then break off at the same 


freezing point, or zero of the scale, 


SCALES OF TEMPERATURE. 


13 


point of the tube at which the last united to the column, 
and the column being shorter in this case, the pellet will be 
shortened by an equal amount. By carefully repeating this 
process we can remove a very short pellet. 

All thermometers pretending to accuracy should be 
graduated on the glass tubes themselves, and not on a scale 
which can be detached from the instrument. 

It has been remarked (Art. 9) that the expansion of the 
mercury with which we have been dealing, is not its actual 
increase of volume, but its apparent expansion when con¬ 
tained in a glass vessel, and is the difference between the 
actual increase of volume of the mercury and that of the in¬ 
terior of the part of the glass vessel which originally con¬ 
tained it. 

18. A thermometer in which the freezing: and boiling: 

o o 

points have been actually determined as above described is 
sometimes called a “ natural standard.” 

Thermometers with capacious bulbs and fine tubes and in 
which, therefore, a small change of temperature produces a 
considerable change in the length of the column of mercury, 
are called “ open range thermometers.” 

Thermometers whose bulbs are very small and thin, and 
which, therefore, quickly assume the temperature of the 
body in which they are immersed, are called “ sensitive 
thermometers.” 

ID. It is very important to be able to convert tem¬ 
peratures expressed in one of the three above-mentioned 
scales, into the corresponding temperatures of either of the 
other scales. 

Suppose F°, G°, and 72° to represent the scale-reading 
of Fahrenheit’s, the Centigrade, and Reaumur’s thermo¬ 
meters respectively, corresponding to any, the same, given 
temperature. Now the freezing point on Fahrenheit’s scale 
is marked 32°. Hence F— 32 is the number of degrees Fah¬ 
renheit of the given temperature, above the freezing point 
while G and R express the same in degrees of the Centi¬ 
grade and Reaumur’s scales respectively. But the excess 
of the temperature of the boiling point above that of the 


14 


SCALES OF TEMPERATURE. 


freezing point is 180°, 100°, and 80° on the three scales 
respectively, and the excess of any other temperature above 
that of the freezing point expressed in degrees of these 
scales, will therefore be proportional to these numbers. 
Therefore F- 32 : G : R :: 180 : 100 : 80. 


We have therefore the following rules:— 

(I) Since O : R :: 100 : 80 :: 5 : 4, in order to convert 
temperatures on the centigrade scale into corresponding 
temperatures on Reaumur’s scale, multiply by , 4 and di¬ 
vide by 5. To perform the inverse process, i.e. to convert 
degrees Reaumur into degrees centigrade, multiply by 5 and 
divide by 4. 

(II) Since F— 32 : C :: 180 : 100 :: 9 : 5, in order to 
convert temperatures expressed in Fahrenheit’s scale into 
the corresponding centigrade temperatures, subtract 32 from 
the reading of Fahrenheit’s scale, and multiply the result 
by 5 and divide by 9. To perform the inverse process, 
multiply the reading of the centigrade scale bv 9, divide by 
5 and add 32. 


For example, 

212° F. = 

55° C. = (| 55 + 32)° F. = (99 + 32)° F. = 131" F. 


212° F. = | (212 - 32)° C. = 1180° C. = 100° C. 


(Ill) Since F-32 -.R :: 180 : 80 :: 9 : 4, in order to 
convert readings of Fahrenheit's scale into the corresponding 
readings on Reaumur’s scale, and vice versa, proceed as in 
rule (II) only replacing the 5 by 4. Thus 

212° F. = s (212 - 32)° R. = £ 180° R. = 80° R. 

y y 

44° R. = (| 44 = 32 )° F. + (99 + 32)° F. = 131° F. 

It may be useful to remark that certain temperatures 
on Fahrenheit’s scale, in addition to the freezing and boiling 
points, have received particular names; for example, 55° F. 
is marked temperate , 76° F. summer-heat , and 98° F. hlood- 
lieat. 


SCALES OF TEMPERATURE. 


15 


The student unaccustomed to such calculations will find 
it useful to work out the following examples. 

Express in degrees Centigrade the following temperatures: 


1. 

56° R. 

Ans. 

70° C. 


77° F. 


25° C. 

3. 

59° F. 

yy 

15° G 

4. 

329° F. 

yy 

165° G 

5. 

* 56“ F. 

yy 

13'3“ G 

6. 

98° F. 

yy 

36'6° C. 

7. 

108° F. 

yy 

42-2" G 

8. 

10° F. 

yy 

— 122"G 

Express in degrees Fahrenheit: 



1. 

56" R. 

Ans. 

158" F. 

2. 

40° C. 

yy 

104° F. 

3. 

60° C. 

yy 

140" F. 

4. 

— 40° G 

yy 

- 40" F. 

5. 

—10" G 

yy 

14° F. 

G. 

309" G 

yy 

588-2" F. 


20. Coloured sulphuric acid is sometimes used instead 
of mercury for filling thermometers, it having the advan¬ 
tage of expanding more for a given change of temperature, 
and thus allowing a wider tube to be employed, so that 
the surface is more distinctly visible. Coloured alcohol is 
employed for very low temperatures, since mercury solidi¬ 
fies at about — 39° C. Alcohol is also used in minimum 
thermometers, which will be presently described. When 
liquids other than mercury are employed, the thermometers 
are generally graduated by comparing them with a standard 
mercurial thermometer at various temperatures, and sub¬ 
dividing the tube between the graduations so obtained, and, 
in the case of the alcohol thermometer, marking off, on the 
portion of the tube which corresponds to temperatures below 
those measurable by the mercurial thermometer, divisions 
equal to the lowest of those which can be directly deter¬ 
mined by the latter instrument. 


16 


SCALES OF TEMPERATURE. 


21. It has been stated (Art. 8) that the scale of the mer¬ 
curial thermometer is a purely arbitrary scale, depending on 
the peculiar properties of mercury and the crown-glass en¬ 
velope in which it is enclosed. This may be rendered very 
apparent by filling several thermometers with different 
liquids, accurately marking off the freezing and boiling 
points upon each, and dividing the tubes between these 
points each into 100 equal parts, as in the construction of 
the ordinary Centigrade thermometer. On placing these 
thermometers in water at various temperatures, it will gene¬ 
rally be found that no two of them precisely agree in their 
indications, except at the freezing and boiling points. If one 
of the thermometers contain water, when the mercurial ther¬ 
mometer registers 4° C., the water thermometer will stand 
below zero, and when the mercurial thermometer is at 16° 
the water thermometer will register about 1°. 

It should be noticed that the discrepancy between these 
different thermometric scales is not due simply to one liquid 
expanding more or less than another but to the different liquids 
expanding according to different laws, so that those intervals 
of temperature which produce equal increments of volume in 
one liquid do not correspond to equal increments in the 
volume of the other; hence if one liquid be supposed to 
expand uniformly as the temperature rises, the rate of ex¬ 
pansion of the other liquids will either increase or diminish 
with increase of temperature, or it may sometimes increase 
and at other times decrease for the same liquid. 

22. Although different liquids indicate different scales 
of temperature, yet there is a class of bodies, viz., those which 
have until recently been regarded as permanent gases, which 
all expand very nearly according to the same law, and there¬ 
fore indicate nearly the same scale of temperature. This 
joint testimony in favour of this particular scale affords a 
good reason for preferring it to any other, and additional 
reasons will be mentioned hereafter* which conspire to render 

* This scale of the air thermometer possesses also another peculiarity, 
viz. that the same amount of heat is required to raise the temperature of a 
given mass of air at constant pressure through each degree of the scale, 
and it nearly agrees with the absolute thermometric scale deduced from 
certain thermodynamic considerations briefly referred to in Art. 8 and 
in Chapter X. 


SCALES OF TEMPERATURE. 


17 


this scale peculiarly valuable. Now this scale of tempera¬ 
ture, generally known as the scale of the air thermometer, 
differs very slightly indeed from that indicated by the ex¬ 
pansion of mercury in a crown-glass envelope, and this of 
itself affords sufficient reason why mercury should be pre¬ 
ferred to other liquids for the construction of thermometers. 

23. The other reasons for the employment of mercury 
in thermometers are: 

(1) It readily transmits heat through its substance (i.e. 
is a good conductor), and thus quickly takes up the tem¬ 
perature of the body in which it is placed. 

(2) Compared with other liquids it requires very little 
heat to raise its own temperature through a given range (i.e. 
its specific heat is small), and this not only favours its quickly 
assuming the temperature of-the body surrounding it, but 
also enables it to come into thermal equilibrium with the 
surrounding body without changing the temperature of the 
latter to any great extent. 

(3) It remains liquid at ordinary pressure through a 
very great range of temperature, viz. from — 39° C. to 350° C. 

(4) It can readily be obtained in a state of purity. 

(5) It does not wet the glass envelope in which it is 
placed. 

24. When mercurial thermometers of extreme accuracy 
are required for scientific purposes their indications are some¬ 
times compared with those of the air thermometer and a 
table of corrections made, so that temperature can be de¬ 
termined by them as nearly as possible in accordance with the 
scale of the air thermometer. Some of the forms of the last- 
mentioned instrument will be described in Chapter IY. 

Throughout the remainder of this work all temperatures 
will be expressed in degrees of the mercurial thermometer, 
except when otherwise stated. 

25. The maximum thermometer is an instrument used 
for registering the highest temperature to which it has 


18 


MAXIMUM AND MINIMUM THERMOMETERS. 


been exposed since it was last adjusted. 

Rutherford’s maximum thermometer 
consists of an ordinary mercurial ther¬ 
mometer, in the tube of which is placed 
a small index, or needle, of black glass 
or enamel, represented by a b in fig. 3, which shews a section 
of the tube in the neighbourhood of the index. The thermo¬ 
meter is kept horizontal, and when the mercury expands its 
convex surface c pushes the index before it, for the same 
reason for which the surface of water is capable of supporting 
a fine dry needle. When the mercury contracts it leaves the 
needle behind as shewn in the figure. The end a of the 
needle will therefore always indicate the highest temperature 
to which the instrument has been exposed since it was last 
adjusted. To adjust the instrument the index is brought 
back into contact with the mercury by placing the thermo¬ 
meter in a vertical position. 

26. The minimum thermometer is employed to register 
the lowest temperature to which it has been exposed. Ruther¬ 
ford’s minimum thermometer consists 
of an alcohol thermometer, placed hori¬ 
zontally, and containing in its tube a 
small index of glass, or enamel, as shewn 
in fig. 4. Since the alcohol wets the 
glass its surface will be concave as shewn at c instead of con¬ 
vex as in the case of mercury. When the alcohol contracts 
the surface c pushes the index back with it, but when it ex¬ 
pands, the index being entirely wetted by the spirit, it is 
left behind. The end a of the index will then shew the 
lowest temperature to which the thermometer has been ex¬ 
posed. The instrument is set by inclining it until the index 
slides down to the surface, c, of the spirit. 

27. In Phillips’ maximum thermometer the column of 
mercury is divided, so that a short thread is separated from 
the rest of the column by the introduction of a small quantity 
of air. When in use the tube is placed in a horizontal posi¬ 
tion, but in order to set the instrument it is held with the 
bulb downwards and gently tapped. By this means the 
separated thread of mercury is caused to fall towards the 


Fig. 4. 


Fig. 3. 









MAXIMUM AND MINIMUM THERMOMETERS. 19 

rest of the column, and to compress the air between the two 
until the length of the tube occupied by the air is (in general) 
not more than one-twentieth of an inch. When the tube is 
placed in a horizontal position and the temperature is raised 
so as to cause the mercury to expand, the pressure of the 
bubble of air pushes the thread of mercury before it, so that 
the end of the thread indicates the highest temperature at^ 
tained; but when the temperature is lowered and the mer¬ 
cury contracts, there being no air in the portion of the bulb 
which is beyond the thread of mercury, there is nothing to 
force the thread back, and it remains stationary, indicating 
the highest temperature which the thermometer has expe¬ 
rienced since it was last set. 

28. Of all self-registering thermometers perhaps the 
best known is Six’s, which serves at once as a maximum 
and minimum thermometer. The bulb A (Fig. 5) is filled 
with spirit. The thermometer tube is bent, as 
shewn in the figure, and contains a quantity of 
mercury which occupies about half the entire 
length of the tube. Above the surface G of 
the mercury is placed a second quantity of spirit 
which flows into the bulb D when the tempera¬ 
ture is sufficiently raised. The only object of 
this spirit is to facilitate the motion of the index 
which registers the highest point to which the 
surface G of the mercury has risen. Two scales 
are provided, one for the surface B , and the 
other for G. Each index is made of iron or 
steel, surrounded by glass and having a fine 
glass fibre attached which serves as a spring 
and, pressing on the interior of the tube, enables 
the index to be supported by friction. (See 
Fig.) When it is required to adjust the instru¬ 
ment for use the indices are drawn down the 
tube by a magnet till they are in contact with 
the mercury. As the mercury moves on account 
of the expansion or contraction of the alcohol in 
the bulb A, the needle at G or B is pushed up the 
tube by the surface of the mercury, as in Rutherford’s maxi¬ 
mum thermometer. Thus the lower surface of the index in 

2—2 















20 


MAXIMUM AND MINIMUM THERMOMETERS. 


the tube CD marks the highest temperature to which the 
bulb A has been exposed, while the index in AB registers 
the lowest temperature. The motion of the surface G is due 
to the expansion of the alcohol together with that of the 
mercury, so that the degrees of the maximum scale ought to 
be a little longer than those of the minimum scale, but this 
difference is not sensible. 


29. The weight-thermometer may frequently be em¬ 
ployed as a convenient form of maximum thermometer, but 
this will be described when we speak, of the expansion of 
liquids (Art. 80). 

&G>er-i ' tt 

^ f^cUstiut-x*.') 


'N 


CHAPTER II. 


ON HEAT CONSIDERED AS A QUANTITY. SPECIFIC HEAT. 

CALORIMETRY. TABLE OF SPECIFIC HEATS. 

30. Def. A quantity is that which can he expressed as 
a multiple, part, or parts of an arbitrary unit of its own kind. 

The complete representation of a Physical quantity will 
therefore consist of two factors, one of which expresses the 
unit, which must he of the same kind as the quantity con¬ 
sidered, while the other is a pure number expressing the 
ratio which the quantity bears to that unit, and is called the 
measure of the quantity. [From this it will be seen that 
a quantity can be measured when its ratio to a definite 
quantity of the same kind can be determined. Now the 
determination, of the ratio which one quantity bears to 
another, regarded as a process of division, is but the inverse 
of multiplication and is possible if the latter operation can 
be performed upon the quantities. But the multiplication 
of a quantity by a pure number is possible whenever the 
operation of adding together two or more quantities of the 
same kind as that considered is capable of a rational inter¬ 
pretation, and hence it follows that the test of quantity 
properly so called, that is, a measurable quantity, is the 
possibility of giving a rational interpretation to the result 
obtained when it is added to another of the same kind.] 

31. In the preceding Chapter we have discussed the 
modes of measuring temperature, and we have throughout 
spoken of degrees , and not quantities , of temperature; 
because hitherto we have seen in temperature only a 


22 


HEAT AS A QUANTITY. 


quality which affects bodies, and not a quantity which can 
be dealt with by the ordinary laws of arithmetic, for in so 
far as we have at present discussed temperature we can 
assign no meaning whatever to the operation of adding 
together two temperatures, or of multiplying a temperature 
by any number. If we mix together two equal quantities of a 
substance at the same temperature, the temperature of the 
mixture is not the sum of the temperatures, but is equal to 
that of either, and if their temperatures be originally unequal, 
the temperature of the mixture is intermediate between that 
of its components. In fact, if we have no other conception 
of temperature than that adopted in the preceding Chapter, 
the operation of adding together two temperatures is alto¬ 
gether unintelligible. At any rate, it is at once obvious that 
we must not add the numbers representing the temperatures 
on any of the arbitrary scales we have described, for the 
results will be different according to the position of the zero 
of the scale, though the temperatures are the same. Thus 
15° C. is the same temperature as 59° F., and 20°'C. the same 
as 68° F., but 35° C. is not the same as 127° F., but is equal 
to 95° F. Temperature is in this respect analogous to many 
other qualities possessed by bodies, as, for example, hardness. 
We may say that a body A is harder than a second body B 
if A will scratch B, but cannot be scratched by it, and we 
may then select a number of bodies, each of uniform hard¬ 
ness, and number them so as to form an arbitrary scale. 
The number attached to each substance will then represent 
its degree of hardness. We may, for example, take the 
hardnesses of the following substances as the standards of 
reference for our arbitrary scale, calling that of Talc 1, Rock- 
salt 2, Calcareous spar 3, Fluor spar 4, Apatite 5, Felspar 6, 
Rock-crystal 7, Topaz 8, Corundum 9, Diamond 10. Now, 
suppose a piece of glass will scratch Apatite but is scratched 
by Felspar, we say then that its degree of hardness lies 
between 5 and 6. Again, suppose a penknife will scratch 
Felspar but not Rock-crystal, then we say that its hardness 
lies between 6 and 7. We cannot however assign any mean¬ 
ing to the operation of adding together the hardness of the 
glass and knife, and so can never have to determine whether 
the result would be a hardness greater than that of the 
diamond or of any other substance, nor can we compare the 


HEAT A PHYSICAL QUANTITY. 


23 


interval between the hardnesses of any two substances in our 
scale with the corresponding interval for any other pair. 

32. The case is however different with the agent which 
is the cause of increase of temperature in bodies, namely, 
heat itself. If we take a pound of water at 1° C. it will 
require a certain definite amount of heat to raise its tem¬ 
perature to 2° C. under given conditions, and a second pound 
of water will require an equal amount of heat to produce the 
same change of temperature under the same circumstances. 
Consequently the two pounds require twice the amount of 
heat required by the one pound to produce the same change 
of temperature, so we see that heat must be of the nature of 
a physical quantity which is subject to the ordinary opera¬ 
tions of arithmetic (i. e. addition, subtraction, &c.), and we 
are therefore justified in speaking of amounts , and not of 
degrees , of heat. 

33. Since, then, heat is a physical quantity, it is of im¬ 
portance to compare the amounts of heat required to pro¬ 
duce given changes in definite portions of matter. If a 
pound of water at 0° C. be mixed with a pound of water at 
2°C. the mixture will be found to have a temperature of 
1°C., so that the heat which leaves 1 lb. of water when its 
temperature falls from 2°C. to 1°C. is just capable of raising 
the temperature of 1 lb. of water from 0°C. to 1°C. We 
learn, therefore, from this experiment, that the same amount 
of heat is required to raise the temperature of 1 lb. of water 
from 1°C. to 2°0. as from 0°C. to 1°C., and therefore the amount 
of heat required to raise 1 lb. of water from 0° C. to 2° C. is 
twice that required to raise it from 0° C. to 1° C. Similarly if 
we mix together 1 lb. of water at 0° C. and 1 lb. at 4° C. the 
temperature of the mixture will be found to be 2° C., from 
which we infer that the amount of heat required to raise 1 lb. 
of water from 2° C. to 4° C. is equal to that required to raise it 
from 0° C. to 2° C. ; whence it follows that the amount of heat 
required to raise 1 lb. of water from 0° C. to 4° C. is four 
times that required to raise it from 0°C. to 1°C. If we 
proceed in this way with water at higher temperatures we 
shall find that the temperature of the mixture is rather 
higher than the mean of its components. Thus if we mix 


24 


UNIT OF HEAT. 


1 lb. of water at 0°C. with 1 lb. at 80° C. the temperature of 
the mixture will be about 4014° C.; from which we infer that 
the amount of heat required to raise a pound of water 1° C. 
when at a high temperature is rather greater than that 
required to raise it 1° C. at a low temperature. If, however, 
the temperature of the water be not high, we may say that 
the amount of heat required to raise the temperature of 
a pound of water through iV°C. is N times the amount 
required to raise the same quantity of water from 0° C. 
to 1°C. 

34. As stated in Art. 30, the expression of any physical 
quantity consists of two factors, one of which is the unit in 
terms of which it is measured, and of the same nature as 
the quantity considered, while the other is a pure number 
shewing how many times the quantity contains this unit, 
and is called the measure of the quantity. 

Hence, in order to express the magnitude of any physical 
quantity we must fix upon an invariable unit of its own 
kind. 

Def. The unit of heat is the amount of heat required to 
raise the temperature of 1 lb. of water from 0°(7. to VC. 
This quantity of heat is sometimes called a calorie. 

In nearly all formulae pertaining to Physical quantities 
it is the measures alone which are represented by symbols, 
the units being either supposed to be understood or else 
expressed in words. Hence these symbols may be treated 
as pure numbers. Since, however, the measures of quantities 
change when the units are altered, in order that an equation 
may be true independently of the particular units adopted, 
the quantities represented on the two sides of an equation 
must be of the same nature. 

35. Def. The specific heat of a substance at any tem¬ 
perature is the ratio of the amount of heat required to raise 
the temperature of any mass of the substance VC. from the 
given temperature , to the amount of heat required to raise the 
temperature of an equal mass of water from 0° C. to 1°C. 

From this definition it will be seen that the specific heat 
of a substance at any temperature is equal to the number of 


CAPACITY FOR HEAT. 


25 


units of heat required to raise the temperature of one pound 
of the substance 1° C. from that temperature. 

The number o f units of heat required to raise the tempera¬ 
ture of a body 1° C. is called its capacity for heat. 


Fig. 6. 


36. From these definitions it will be seen that the 
specific heat of a body depends only on the kind of matter 
of which it is composed and the physical conditions under 
which it is placed, while the capacity for heat of a body is 
proportional to the amount of matter it contains. The fact 
that equal volumes of different metals have different capa¬ 
cities for heat may be shewn experimen¬ 
tally by heating a number of equal spheri¬ 
cal balls of different metals, say copper, 
iron, tin, zinc, lead, and bismuth, to 100°C., 
and then laying them on a thin cake of 
wax. The copper ball will quickly melt 
its way through the wax and be followed 
almost immediately by the iron ball, the 
copper preceding the iron because, though 
its specific heat is only *095 while that 
of iron is T13 (per unit of mass), yet the 
density of the copper is greater than that 
of the iron, and the copper also more 
readily allows of the passage of heat from 
its interior. Shortly after the iron, the 
zinc ball, whose specific heat is '0955, will 




fall, while the lead, whose specific heat is ’03, and the tin, 
whose specific heat is ‘056, will perhaps be unable to melt 
their way through, and the bismuth ball, whose specific heat 
is nearly the same as that of lead but whose density is much 
less, will only make a comparatively shallow impression in 
the wax. 


37. Referring to the properties of water mentioned in 
Art. 33, it will be seen that the specific heat of water is 
nearly unity, if its temperature be not much above 0°C., 
but at higher temperatures its specific heat is rather greater 
than unity. It continues to increase with the temperature. 
(Art. 52.) 












26 


CALORIMETRY. 


38. The operation of measuring quantities of heat is 
called calorimetry; and an instrument adapted to this pur¬ 
pose is called a calorimeter. 

The process of determining the specific heat of a sub¬ 
stance, consists in finding the amount of heat required to 
produce a given change of temperature in a known mass 
of the substance, and is therefore an operation in calori¬ 
metry. We shall now describe some of the methods usually 
adopted for measuring quantities of heat. 


The Method of Mixture. 

39. An illustration of this method has already been 
given, when we shewed how to prove experimentally that the 
amount of heat required to raise the temperature of a pound 
of water from 1° C. to 2° C. was equal to the amount required 
to raise an equal mass of w r ater from 0° C. to 1° C. It consists 
essentially in mixing together known quantities of two sub¬ 
stances at different temperatures, the specific heat of one 
of which is known, and determining the temperature of 
the mixture. In most cases w r ater is taken as the substance 
whose specific heat is known; the other substance may be 
a liquid or a solid, but it must not act chemically on the 
water. The method will be. best understood by taking 
another example. 

40. Suppose we wish to determine the specific heat- of 
copper. We weigh out a convenient quantity, say 500 
grains, of copper and suspend it, by a fine thread, in the 
steam above the surface of water boiling in a vessel almost 
closed, but allowing sufficient means of egress for the steam 
to prevent its pressure becoming sensibly greater than that 
of the atmosphere. If the barometer stand at 30 inches, the 
copper wfill after some time have acquired a temperature of 
about 100° C. While the copper is being heated we weigh 
out carefully a quantity of distilled water, say 1000 grains. 
This is placed in a vessel whose capacity for heat is small, 
and after the vessel and water have acquired the same 
temperature, this temperature is very carefully observed. 
Suppose it to be 12° C. The copper is now removed from 


SPECIFIC HEAT OF COPPER. 


27 


its hot bath and plunged as quickly as possible into the cold 
water, where it is moved up and down by means of its 
suspension thread, until thermal equilibrium between it and 
the water is attained. (It is important that this process 
should require as short a time as possible, and to this end 
the copper should not have a very small surface. A coil of 
copper wire answers the purpose very well.) The temperature 
of the water is then again carefully observed; and the time 
elapsing between the immersion of the copper and the ob¬ 
servation of this temperature should also be noticed. Suppose 
the temperature to he 157°C. The ratio of the mass of the 
copper to that of the water in the calorimeter should, if 
possible, be so arranged that the temperature of the air in 
the room is intermediate between the first and last observed 
temperatures in the calorimeter, and somewhat nearer to the 
latter than the former. This can be insured if the specific 
heat of copper be known approximately. The loss of heat 
by radiation and conduction from the instrument will then 
be corrected by a nearly equivalent gain, but in extremely 
accurate measurements this must be determined and allowed 
for. This condition would be fulfilled in the case we are 
considering, if the temperature of the air in the room were 
between 14° C. and 15° C., or even somewhat higher. Now if 
we neglect the capacity for heat of the vessel containing the 
water, we have sufficient data to obtain a rough approximation 
to the specific heat of copper. The number of degrees of 
temperature lost by the 500 grains of copper is 100 — 157 or 
84’3, and the heat leaving the copper serves to heat 1000 grains 
of water 37° C., and would therefore heat 500 grains of water 
7*4° C. The mean specific heat of copper between the tem¬ 
peratures 157° C. and 100° C. is therefore ^^ = *0877... 

41. The result just obtained is, obviously, too small, 
because we have neglected the heat taken up by the vessel 
containing the water, when the temperature of the latter is 
raised. In order to determine this approximately, we may 
refill the vessel with cold water, and after allowing it to stand 
for a considerable time, observe its temperature. Suppose 
it again to be 12°C. Now empty the vessel as thoroughly 
as possible, and place in it 1000 grains of water at say 15°C., 


28 


SPECIFIC HEAT OF COPPER. 


this temperature being accurately observed before pouring 
the water into the vessel. After this has stood for some 
time, say rather less than the time above referred to, let the 
temperature be again observed. Suppose it to be 14*77° C. 
Now the amount of water at 12° C., which must be mixed 
with 1000 grains at 15° C. to reduce the whole to 14*77°C. 
is about 83 grains. The presence of the vessel then is 
equivalent to increasing the amount of water from 1000 to 
1083 grains. Making allowance for this, we see from the 
results just obtained, that the amount of heat required to 
raise the temperature of 500 grains of copper 84*3 degrees, 
will raise 1083 grains of water 3*7 degrees; and will there¬ 
fore raise the temperature of 500 grains of water 

/3*7 x 1083\° n 

\ 500 ) 


The mean specific heat of copper between 15*7°C. and 100°C. 
is therefore 


3*7 x 1083 
500 x 84*3 


*095... 


This result is very nearly correct. 


As another example of this method the student may take 
the following:— 

1000 grains of mercury at 100° C. are mixed with 1000 
grains of water at 15° C. contained in a vessel , which, on 
account of its capacity for heat, is equivalent to an increase 
of 100 grains in the quantity of water within it. The result¬ 
ing temperature is 17*5° C. Find the specific heat of mercury. 

Ans. *033. 


42. Notwithstanding the precautions we have mentioned 
and the corrections we have applied, there are still some 
sources of error incidental to the above method which con¬ 
tinue to vitiate our results. Two notable sources of error are, 
(1) the condensed steam which clings to the substance and 
is conveyed with it into the calorimeter, thus increasing the 
apparent value of the specific heat, and (2) the loss of heat 
while passing from the heater into the calorimeter. Both 
these sources of error are eliminated in the following method, 




SPECIFIC HEAT. 


29 


which will be found to give tolerably accurate results. The 
apparatus is represented in figure 7. The calorimeter, C, is a 

Fig. 7. 



/f. . ^ 


cylindrical vessel made of thin copper and polished or electro¬ 
plated on the outside in order to diminish radiation from the 
surface. This is suspended by silk strings within a second 
copper vessel, D, which is polished or plated on the inside 
so as to reflect any radiation it may receive from the calo¬ 
rimeter. This vessel is closed by a lid having in its centre 
a hole sufficiently large to allow the body whose specific heat 
is to be measured to pass through it into the calorimeter. 
By this means the loss of heat from the calorimeter is re¬ 
duced to a minimum, while the temperature of the copper 
vessel, G, never differs sensibly from that of the water within 
it, and the heat absorbed by it can therefore be accurately 
determined and added to that absorbed by the water within 
it. The heater, which is a modification of that of Regnault, 
consists of a thin copper tube AB , surrounded by a large 
tube EF , the space between them being closed at the top 






































30 


METHOD OF FUSION. 


and bottom but communicating at E with a steam boiler, 
while at F there is a tube for the escape of the steam. The 
whole apparatus rests upon a board, and is capable of turn¬ 
ing about the vertical pillar GH, which serves as a guide, 
when it is required to bring the opening of the tube verti¬ 
cally over the hole K in the board in order to drop the 
substance into the calorimeter. For this purpose the latter 
is quickly brought under the hole K and removed again as 
soon as possible, the board in the meanwhile serving to 
screen the calorimeter from radiation from the steam-jacket. 
The tube AB is open at the bottom, the board itself serv¬ 
ing to close it except when it is brought over the hole K ; 
but the top is closed by a cork through which passes a ther¬ 
mometer, T, and a glass tube of very fine bore which admits 
the passage of a fine silk thread by which the body, P, to be 
heated is suspended. After the steam has been turned on 
it should be allowed to blow through the steam-jacket for 
some time after the thermometer has become perfectly steady, 
in order to ensure the body P having the same temperature 
as the thermometer throughout its substance. The tempe¬ 
rature of the water in G having been observed, the calo¬ 
rimeter is quickly brought beneath the hole K f while the 
tube AB is brought over it and the body P lowered into the 
water by means of the thread. The calorimeter is then 
removed and the measurement completed as in the case 
above described. 


The Method of Fusion. 

43. If we mix together 1 lb. of water at 79° C. with 1 lb. 
of water at 0° C., we obtain 2 lbs. of water at very nearly 
39-5° C. If, however, we mix together 1 lb. of water at 79° C. 
with 1 lb. of ice at 0° C., we obtain 2 lbs. of water at 0° C. 
From this we see that in order to melt 1 lb. of ice at 0° C. 
without changing its temperature, we require as much heat as 
would raise lib. of water 79°C., in other words, we require 
79 units of heat. This number, 79, is called the latent heat 
of water, or the latent heat of fusion of ice, and will be more 
fully discussed in a subsequent chapter; it is introduced 
here because this property of ice is made the basis of the 


ICE CALORIMETER. 


31 


construction of several instruments for measuring quantities 
of heat, known as ice calorimeters , two of which we shall 
now describe. We must so far trespass upon the matter of 
subsequent chapters as to state, that while pure ice is melt¬ 
ing under ordinary pressure, the temperature of the ice and 
water remains accurately at 0° C. till the whole of the ice is 
melted, a fact of which we have already availed ourselves in 
determining the freezing-point. 

44. The calorimeter of Laplace and Lavoisier consists 
of three vessels. The inner vessel A is 
formed of thin copper and contains the 
heated body. This is placed in the in¬ 
terior of a larger vessel, B, which forms 
the calorimeter proper, the space be¬ 
tween them being filled with broken ice, 
and this again is placed within a still 
larger vessel, also packed with broken 
ice to prevent absorption of heat from 
surrounding bodies by the calorimeter 
proper. A small pipe passes through 
the outer vessel from the bottom of the 
calorimeter proper, and serves to convey 
the water from B into a vessel placed for its reception. 
Now since B is surrounded by ice at 0° C. the ice within it 
can only melt by taking up the heat which passes from the 
body in A, and since 1 lb. of ice requires 79 units of heat to 
melt it, we can determine the amount of heat which leaves 
the body in A, by weighing the water which falls into 
the vessel D. The body in A is of course finally reduced 
to the temperature of the ice in B } that is, to 0° C. The 
pipe F simply conveys away the waste water from the ice 
jacket produced by the heat absorbed from surrounding 
bodies. 

45. Suppose the body in A to be 500 grains of copper 
originally at 100° C., and suppose that the flow of water from 
B ceases when 60 grains have escaped. We know that 
the temperature of the copper is then 0° C. Now the heat 
required to convert 60 grains of ice at 0° C. into water at 
the same temperature, would raise 78 x 60 grains, or 4740 
grains, of water 1° C. Hence the heat lost by 500 grains of 








32 


bunsen’s calorimeter. 


copper in cooling from 100° C. to 0° C. would raise 4740 
grains of water 1° C. The mean specific heat of copper 

* 4740 

between 0° C. and 100° C. is therefore --- - = *0948. 

500 x100 

46. The action of Bunsen’s Calorimeter depends on the 
fact that ice contracts considerably when melting, and the 
water continues to diminish in volume as its temperature 
increases between 0° C. and 4° C. It consists of a vessel, 
A, containing water, into the upper part of 
which a test-tube, B, is sealed, and the 
whole vessel is thus closed except for the 
fine tube C, which is graduated, and, to¬ 
gether with the lower part of A , filled with 
mercury. When the instrument is to be 
used it is immersed in melting snow or 
ice till the temperature of the water has 
fallen to 0° C. when a quantity of alcohol, 
cooled considerably below the freezing- 
point by a mixture of ice and salt, is 
poured into the test-tube which causes a layer of ice to be 
formed round the tube while the mercury is forced along 
the tube G on account of the expansion of the water in 
freezing. Sometimes ether is placed in the test-tube and a 
current of cold air blown through it which causes evaporation 
to take place so rapidly that the temperature falls below 
the freezing-point. The alcohol or ether is then removed, 
and cold water is placed in the test-tube, and when it has 
attained a temperature of 0° C., as indicated by the surface 
of the mercury in the tube G becoming stationary, the 
position of the surface in G is observed. The body whose 
capacity for heat is to be measured, having been heated to 
100° C. in steam, is now placed in the test-tube B. This 
heats the water in B, which in its turn communicates the 
heat to that in A, thus melting some of the ice and causing 
the surface of the mercury in G to move. The decrease in 
the volume of the contents of A is measured by the move¬ 
ment of the mercury in G, and thus the amount of ice melted 
in A can be found. Also no heat can have entered A except 
from the test-tube, since it is surrounded by melting snow, 
and nearly all the heat lost by the body in B will enter A, 









bunsen’s calorimeter. 


33 


for most of the water in B being at 0°C., since water con¬ 
tracts in volume as its temperature rises from 0°C. to 4°C., 
that warmed by the hot body is heavier than the rest , and 
does not rise to the surface. The amount of ice melted in A 
therefore enables us to measure the heat lost by the body 
in B in cooling from 100° C. to 0°C. Several measurements 
can be made with the instrument without again freezing the 
water which surrounds the tube. 

47. An improved method of employing Bunsen’s Calo¬ 
rimeter has recently been suggested. Instead of employing 
a long tube calibrated throughout its length, the tube C is 
bent over and the end rounded off while the bore is made to 
terminate in a very fine aperture. The end of the tube, 
which is completely filled with mercury, is made to dip into 
a small cup of mercury which is weighed before and after each 
experiment, and as the ice melts more mercury enters the 
calorimeter through the aperture at the end of the tube. 
The amount of mercury thus entering is determined by the 
loss of weight of the cup of mercury. 

48. Other forms of calorimeters have been employed for 
the measurement of the specific heats of gases and liquids. 
The most perfect are those devised by Regnault. In order 
to determine the specific heat of a gas at constant pressure, 
he made a known quantity pass from a holder through a 
metal “ worm ” which was immersed in heated oil. In this 
it acquired the temperature of the oil, and thence it passed 
through a complicated metal vessel immersed in the water of 
the calorimeter. Here it acquired the same temperature as 
the water, while the temperature of the latter was gradually 
raised. The temperature of the water being observed at 
the commencement and close of the experiment, after making 
proper correction for the capacity of the apparatus, the num¬ 
ber of units of heat given up by the gas to the calorimeter 
could be found. Now all the gas was heated to the tempe¬ 
rature of the oil, while the temperature to which it was 
cooled in the calorimeter was variable. Since however the 
temperature of the calorimeter must have increased almost 
uniformly, the result was the same as if the whole of the gas 
had been cooled to the temperature which is the arithmetical 


34 


regnault’s calorimeters. 


mean of the initial and final temperatures of the calorimeter. 
Knowing the mass of the gas, we have now sufficient data 
for the calculation of its specific heat. 

49. The principal peculiarity of Regnault’s calorimeter 
for liquids is the artifice for preventing loss of heat by the 
liquid, on account of exposure in passing from the bath in 
which it is heated to the calorimeter. This consists in forcing 
the liquid by means of atmospheric pressure, from the vessel 
in which it is heated, and which is immersed in a hot bath, 
through a tube into a vessel immersed in the water of the 
calorimeter, the latter instrument being prevented from re¬ 
ceiving heat directly from the hot bath, to which it is 
placed very close, by means of a screen. 

50. We may observe that in the case of substances 
which, like water, are known in the solid, liquid and gaseous 
states, the specific heat of the liquid is greater than that of 
either the solid or the gas, provided the volume of the gas be 
unchanged. 


51. The following table gives the specific heat of some 
well-known substances. The numbers given of course repre¬ 
sent the mean specific heats of the various bodies between 
certain limits of temperature employed in the experiments. 
These temperatures are given in the third column. 


Table of Specific Heats of Metals, &c. 
(Regnault.) 


Bismuth 


*03084 

Centigrade. 

98°—13° 

Lead ... 


*03140 

98°—15° 

Platinum 


•03243 

99°—12° 

Gold. 


•03244 

98°—12° 

Mercury 


•03332 

98°—12° 

Antimony 


•05077 

97°—12° 

Tin . 


•05623 

99°—12° 

Silver 


•05701 

99°—13° 

Copper 


•09515 

98“—15° 

Zinc ... 


•09555 

99°—14° 









SPECIFIC HEAT DEPENDS ON 

EXTERNAL 

CONDITIONS. 35 

Iron ... 

*11380 

Centigrade. 

98°—17° 

Sulphur (native) 

T7760 

99°—14° 

„ (recently melted) 

•20259 

98°—14° 

Phosphorus ... 

•18870 

30°—10° 

Graphite 

*20083 

98°—12” 

Aluminium 

•21430 

97“—14“ 

Magnesium 

•24990 

98"—23" 

Lithium 

•94080 

100°—27° 

Brass ... 

•09391 

98"—12" 

Glass .... 

T8768 

99"—14° 


Table of Specific Heats of Liquids. 

Centigrade. 

Bromine T07 45°—11° 

Sulphuric Acid 343 46°—21° 

Ether -.503 . 

Alcohol *615 43°—23° 


Specific Heats of Gases (at Constant Pressure.) 


Air -2374 

Oxygen *2175 

Nitrogen *2438 
Hydrogen 3‘4090 
Chlorine T210 


Sulphurous Anhydride T544 


Carbonic Anhydride *2163 
Carbonic Oxide *2450 

Nitrous Oxide -2438 

Steam *4805 


52. As a general rule the specific heats of liquids, as 
stated in Art. 50, are greater than those of either gases or 
solids, and the specific heat increases with the temperature. 
Thus the specific heat of water at 0° C. being taken as unity 
its specific heat at 50° C. is T0042; at 100° C., 1*013; and 
at 200° C., P044. The specific heat of ice at temperatures 
near the freezing-point is about ’504. 

53. The methods described in this chapter only enable 
us to measure quantities of heat which pass from one body 
to another, the receiving body being the water, or ice, of 
the calorimeter; they will not enable us to form any idea 
of the whole amount of heat contained in a body, because 
we cannot get the whole of the heat to pass out of any body 

3—2 






36 SPECIFIC HEAT DEPENDS ON EXTERNAL CONDITIONS. 

into another, and if we could the amount would depend 
upon the manner in which the heat is abstracted; whether, 
for instance, the body is allowed to expand and do work, or 
whether it contracts and has work done upon it by some 
agent external to itself. Consequently, if we speak of the 
whole amount of heat contained in a body, we use a phrase 
to which we can assign no meaning, and, as the student 
will learn after studying the effects of heat upon gases, the 
amount of heat required by a body to cause it to pass from 
one given temperature to another frequently varies consider¬ 
ably with the conditions as to pressure, &c. to which it is 
subject, and ifrrbt a definite quantity unless these conditions 
be specified, though its variations are usually extremely small 
in such cases of liquids and solids as we have generally 
to deal with. It was on account of these considerations, 
that in first introducing heat as a measurable quantity, we 
did not say that the whole amount of heat contained in 
two pounds of water at 1° C., was equal to twice the amount 
contained in one pound at the same temperature, but spoke 
of the amount of heat required to raise different quantities 
of water from 1°C. to 2°C. under given conditions. Since, 
in the cases of water and most other liquids and solids, the 
amount of heat required to produce a given change of tem¬ 
perature varies very slightly with ordinary variations of 
external circumstances, the words in italics are generally 
omitted, but this statement will not apply to gases. 


CHAPTER III. 


SOURCES OF HEAT. 

54. We have seen that one effect of hpat upon bodies 
is, in general, to increase their temperature, atfd in Chapter I. 
we have seen how to measure temperature in degrees of an 
arbitrary scale, while in the last Chapter we discussed the 
measurement of quantities of heat. We must now briefly 
enumerate the most frequent sources of heat with which we 
are acquainted, and then consider the effects of heat upon 
bodies. 

55. The principal sources of heat are, 

(I) Radiant energy. 

(II) Chemical action {including combustion). 

(III) Mechanical sources , such as the energy of a me¬ 
chanical system converted into heat by doing work against 
friction, viscosity, pressure (as in cases of impact), &c., or by 
otherwise producing any change in the form or volume of 
an imperfectly elastic body. 

(IY) Electric currents , including those currents which 
are of very short duration, and which are more generally 
known as electric discharges, such as lightning flashes. 

(Y) The magnetisation and demagnetisation of iron or 
other magnetic substances. 

(YI) Change of state , such as the condensation of vapours, 
solidification of liquids, crystallization, or the passage from 
one crystalline form to another. 

(YII) The internal heat of the earth differs from the pre¬ 
ceding sources, inasmuch as the heat exists in the earth as 
heat before it comes under our notice, and is therefore not 
a source from which heat is produced, but simply a store 


38 


SOURCES OF HEAT. 


from which it is derived . Volcanic heat has been applied to 
commercial purposes in the preparation of borax. 

56. (I) Of the above sources of heat the radiation 
from the sun is by far the most important. Radiant energy 
produces different effects according to the nature of the body 
which receives it. If it fall upon sensitised photographic 
paper or plates it decomposes the silver salt; if it fall upon 
our eyes it in some cases produces the sensation of light; 
but by far the most common effect is the production of heat, 
an effect of which we are at once conscious if we stand in 
the sunshine or in front of a fire. The nature and laws of 
radiation will be discussed more at length hereafter. 

57. (II) Chemical action is generally accompanied by 
the production or the absorption of heat. When light is also 
produced the action is frequently called combustion. The 
amount of heat produced depends only on the quantities, 
character, and conditions of the reagents at the beginning 
and end of the operation, if no energy is abstracted from 
or given to the substances by other systems. Thus a certain 
amount of heat will be produced by the combustion of two 
pounds of hydrogen in oxygen, forming 18 pounds of water; 
and if 39 pounds of potassium be brought into contact 
with the water so formed, one pound of hydrogen will be 
liberated and 56 pounds of caustic potash will be produced, 
while a certain additional amount of heat will be generated, 
but the whole quantity of heat produced in the two opera¬ 
tions is the same as if 39 pounds of potassium and one 
pound of hydrogen had been allowed to combine directly 
with 16 pounds of oxygen and with each other. But while 
the whole amount of heat which can be obtained from any 
chemical action, when the acting substances are cooled down 
to their original temperature, depends only on the quantity 
of the substances combining and on the character of the 
action, the temperature produced depends upon the initial 
temperatures of the substances and on the capacity for heat 
of the products among which the heat is distributed. For ex¬ 
ample, if hydrogen burn in air, the heat generated is divided 
between the aqueous vapour produced and the nitrogen 
of the air, but if it burn in pure oxygen the wdiole of the 
heat is at first confined to the aqueous vapour produced, and 


SOURCES OF HEAT. 


39 


hence the oxy-hydrogen flame is capable of readily fusing 
platinum and of producing a much higher temperature than 
can be produced by hydrogen burning in air. 

58. The influence of the initial temperature of the com¬ 
bining substances on the temperature produced is seen in 
the effects of the hot blast as applied to blow-pipes, and 
blast furnaces, and to the Siemens furnace. In the last- 
mentioned furnace the products of combustion are conducted 
into a chamber partly filled with fire bricks, between which 
they have to pass before escaping up the shaft, and in this 
manner the bricks are heated to redness. The draught is 
then turned aside into a second similar chamber while the 
air supplied to the furnace is made to pass through the 
heated chamber, and when the second chamber has become 
sufficiently heated the draught is again reversed so that all 
the air supplied to the furnace is raised to a high tempera¬ 
ture without employing any other than the waste heat of 
the furnace itself. This furnace has been employed in the 
manufacture of steel by the Siemens-Martin process, which 
consists in fusing wrought iron with such a quantity of 
cast iron as shall provide the requisite amount of carbon for 
the steel. 

This same principle of the regenerator has been applied 
by Sir Wm. Siemens to gas-lamps for street lighting and 
other purposes. In these lamps the air before reaching 
the gas flame is made to pass through tubes heated by 
the flame itself and thus the temperature of the flame is 
raised while the intensity of the light is greatly increased 
and its tints rendered more white. 

In order to cause two substances to burn together it is 
generally necessary to raise them above a certain tempera¬ 
ture. If the temperature produced by their combination be 
sufficiently high to inflame them, combustion will continue, 
but otherwise it will cease. The temperature produced by 
ammonia gas burning in air is insufficient to ignite it, so 
that the combustion cannot be maintained without an ex¬ 
ternal supply of heat, but in pure oxygen ammonia will 
continue to burn. The heat of animals is due to the com¬ 
bination of their food with the oxygen of the air. 


40 


SOURCES OF HEAT. 


59. Many calorimeters have been devised for the pur¬ 
pose of measuring the heat produced by chemical action, 
especially by the combustion of different fuels, in which case 
the measurement is of considerable commercial importance. 
In most of these instruments the products of combustion are 
made to pass through a long pipe immersed in water in the 
calorimeter and the change of temperature of the water is 
observed. The heating effect of a fuel may be expressed by 
the number of units of heat produced by the combustion of 
a pound of the fuel. It is, however, frequently stated in 
terms of the number of pounds of water at 100° C. which 
can be converted into steam at the same temperature by the 
combustion of one pound of the fuel, and, as will be stated 
more fully hereafter, to convert a pound of water at 100° C. 
into steam at the same temperature, requires as much heat 
as would raise the temperature of about 536 pounds of water 
from 0°C. to 1°C. 

In Thompson’s Calorimeter, which is sometimes employed 
for comparing the calorific powers of different varieties of 
coal, the coal is finely powdered, mixed with about fifteen 
times its weight of a mixture of nitre and potassic chlorate, 
placed in a crucible within a diving bell and ignited by a 
slow match after lowering the diving bell into a vessel con¬ 
taining a known quantity of water. The products of com¬ 
bustion escaping from the bottom of the bell bubble up 
through the water and are thereby cooled nearly to the 
temperature of the water itself, which temperature is ob¬ 
served before and after the combustion of the coal. The 
heat absorbed by the vessel, the diving bell, &c. is estimated 
and added to that absorbed by the water, the total repre¬ 
senting the heat developed by the combustion of the thirty 
grains of coal. With this apparatus it is difficult to secure 
ihe complete combustion of the coal, but though it may 
not be trusted for exact determinations of the absolute 
amount of heat developed by the coal it is sufficiently accu¬ 
rate for the comparison of the values of different kinds of 
coal as fuel. 

In the experiments of Favre and Silbermann the com¬ 
bustion was carried on in a chamber made of gilded copper 
plate and the oxygen, which had been previously purified, 
was supplied through a tube, while the products of combus- 


SOURCES OF HEAT. 


41 


tion escaped through a long narrow tube which was wound 
several times round the outside of the vessel. The progress 
of the combustion was watched through a window composed 
of a triple disc of glass, alum and quartz, to prevent loss of 
heat by radiation. The combustion chamber with its sur¬ 
rounding coil of tube was immersed in water contained in a 
copper vessel forming the calorimeter, which was silver plated 
on the outside. This was surrounded by a second vessel, 
silver plated on the inside, and the space between filled with 
swan’s down. The calorimeter was closed by a cover through 
which a stirrer passed. The silver plating served to prevent 
loss or gain of heat by radiation. The second vessel was 
surrounded by a third vessel, the intermediate space being 
filled with water to prevent variations of the temperature 
of the air affecting the apparatus. 

60. The amounts of heat developed by the combustion 
in oxygen of one pound of some substances are given in the 
following table. 

Heat of Combustion in Oxygen. 


Substance. 

Units of heat 
evolved. 

Observer. 

Hydrogen 

( 33808 

Andrews 

\ 34462 

Favre and Silbermann 

Wood charcoal 

j 7900 
l 8080 

Andrews 

Favre and Silbermann 

Sulphur 

2307 

Andrews 

Phosphorus 

5747 

>» 

Zinc 

1301 


Iron 

1576 

a 

Copper 

603 

a 

< 2403 

Favre and Silbermann 

Carbonic oxide 

\ 2431 

Andrews 

Marsh gas 

13108 

a 

( 6850 


Ethylic alcohol 

) 7184 

Favre and Silbermann 

Welsh coal 

about 8241 


Newcastle coal 

„ 8220 


Derbyshire coal 

„ 7733 


Wood (dried in air) 

„ 3547 









42 


SOURCES OF HEAT. 


From this table it will be seen that the heat developed 
by the combustion of one pound of coal is capable of con¬ 
verting between 14 and 15 pounds of water at 100° C. into 
steam at the same temperature. 

61. (Ill) Of the mechanical sources of heat friction is 
perhaps the best known. A very common experiment con¬ 
sists in making a button hot by rubbing it against a form, 
and it is no rare occurrence- for a railway axle to become red- 
hot through the supply of grease becoming exhausted or 
otherwise failing in its duty. The bearings of the rollers 
employed in rolling bar iron, and which are subject to very 
great pressure, are kept cool by a stream of water continually 
running over them, and this also serves to lubricate the sur¬ 
faces. Most persons have observed the sparks which fly from 
beneath the wheels of a break-van when the break is ap¬ 
plied so as to prevent their rotation. If a small brass tube 
be filled with water and corked, and be then made to rotate 
rapidly while it is squeezed between two pieces of wood, the 
heat caused by the friction will soon cause the water to boil, 
and to violently eject the cork. Count Rumford raised the 
temperature of 18’77 pounds of water besides a large quan¬ 
tity of metal from 15° C. to 100° C. in 2J hours by means of 
the friction of a blunt borer in a gunmetal cylinder. (See 
Chapter XI.) If a piece of tin be bent in opposite directions 
in rapid succession a crackling noise is heard, and a great 
amount of heat generated. 

62. Heat is developed when work is done by compress¬ 

ing a substance, whether the pressure act for a long time or 
for an exceedingly short time, though in the former case the 
heat, having a long time in which to escape, does not always 
make itself manifest. A few blows with a hammer will 
raise the temperature of a piece of lead very considerably, 
and a dexterous smith may heat a small piece of iron to 
redness by hammering it. The splinters which fly from a 
flint when struck by a piece of hard steel are often at a 

white heat. The impact of a chilled iron shot on an iron 

target produces a great amount of heat together with a 
bright flash of light. If air contained in a cylinder be sud¬ 
denly compressed by the descent of a piston, it may be 


SOURCES OF HEAT. 


43 


readily heated sufficiently to ignite German tinder, or the 
vapour of bisulphide of carbon, previously introduced into 
the cylinder. When a drop of bisulphide of carbon has been 
introduced, the sudden compression of the air is accom¬ 
panied by a bright flash of light. 

63. That heat is developed when work is done against 
the resistance of a body to torsion is readily shewn by the 
following experiment. A brass tube four or five inches in 
length and about fths of an inch in diameter is soldered at 
both ends to cross-pieces, one of which is drilled through so 
that the bulb of a thermometer may be inserted into the 
tube. One of the cross-pieces being fixed in a vice, the 
other is rapidly turned through a few degrees in opposite 
directions successively. The heat generated in continually 
reversing the torsional strain produces in a few minutes a 
very appreciable rise of temperature in the brass tube, which 
is rendered apparent on the insertion of the thermometer. 

The heating effect of a direct shearing strain is conspi¬ 
cuous in the punching of holes in boiler, or other, plates, and 
in the shearing of iron bars. Generally the newly sheared 
surfaces are far too hot to be touched by the hands. 

64. There are a few bodies which contract when heated, 
and expand on cooling. Such bodies become heated when 
caused to expand by an external agent, and heat is absorbed 
by them on contracting. A piece of stretched India-rubber 
when heated contracts in the direction of its tension. This 
may be easily shewn by suspending a weight by means of 
an India-rubber tube, a small piece of glass or metal tube 
being inserted at each end in order that a string may be 
attached without closing the tube. If a current of steam 
be blown through, the India-rubber will contract, thus 
raising the weight, and will expand again as the tube cools. 
If a piece of India-rubber be suddenly stretched and applied 
to the face of a thermo-pile* heat will be at once indicated, 
while if the rubber be allowed to contract, exerting tension 
all the time, the face of the thermo-pile in contact with it 
will be cooled. 


See Chapter VII. 


44 


SOURCES OF HEAT. 


Whenever a body expands on being heated, heat will be 
generated if it is compressed by an external agent, but if 
the body contract when heated, heat will be generated by 
forcibly causing it to expand. 

G5. Whenever work is done or energy lost by a me¬ 
chanical system and there is no form of energy other than 
heat into which it can be converted, the whole of the work 
so done or energy so lost has its equivalent in heat generated 
in the system. This is true whether the bodies we are deal¬ 
ing with are large or molecular, so that we may expect heat 
to be generated whenever a state of strain in any body is 
relieved. 

66. (IV) Whenever an electric current is sent through 
any resistance heat is produced. Dr Joule has shewn that 
the heat produced is proportional to the product of the 
resistance and the square of the current. If a strong cur¬ 
rent be sent through a wire of considerable resistance, but 
whose capacity for heat is very small, the temperature of the 
wire will be very much raised, and it is easy in this way to 
fuse a few inches of fine Platinum wire by the current from 
two or three Grove’s cells. A current may be produced by 
causing a coil of wire to rotate between the poles of a 
magnet, and when the ends of the coil are connected together 
without the introduction of any fine wire, the whole of the 
heat is generated in the coil itself. When a Grove’s, or 
Bichromate, battery has its poles connected by a short thick 
copper wire a great current is produced, and a quantity of 
heat proportional to the square of the current; but nearly 
the whole of this heat is produced in the cell itself. When 
a piece of brass or copper is made to spin between the poles 
of a powerful magnet great resistance to the motion is ex¬ 
perienced, and heat is generated on account of electric 
currents induced in the metal. If iron be employed instead 
of brass, or copper, the iron becomes magnetised first in one 
direction and then in another, and the successive reversal 
of the magnetization adds to the heating effect. If a 
strongly charged Leyden battery be discharged through a 
fine metallic wire stretched on a card, say a foot of wire 
*002 inch in diameter, the wire will be dissipated, forming 


SOURCES OF HEAT. 


45 


a beautiful streak on the card, with here and there a 
system of dark lines radiating from a point which looks 
like a centre of explosion. If the wire be covered with silk 
the latter will remain intact though the wire is dissipated 
between the threads. 

When an electric current passes across the junction of 
dissimilar metals heat may be produced or absorbed accord¬ 
ing to the direction of the current. This is known as the 
Peltier effect. When a current passes along a metal the 
temperature of which varies from point to point heat may be 
absorbed or produced according to the direction of the current 
and the character of the metal. This is known as the Thom¬ 
son effect. (See Chapter VII.) 

(V) If the rapidly alternating currents from an alterna¬ 
ting current dynamo be sent round the coil of an electro¬ 
magnet the iron core becomes rapidly heated, but this is not 
the case if a steady current of the same strength as the alter¬ 
nating currents be caused to flow continuously through the 
coils. The cause of the heating is partly the rapid variation 
of the magnetism of the iron. 

67. (VI) Whenever heat is consumed during any trans¬ 
formation, as when a body passes from the solid to the 
liquid state, heat will be produced when the transformation 
takes place in the opposite direction. Thus heat is given 
out by water in freezing, and if 100 grains of steam at 
100°C. be passed into 536 grains of water at 0°C., we obtain 
636 grains of water at 100°, so that the steam raises the 
temperature of the water by the heat it emits in condensa¬ 
tion without changing its own temperature. 

Certain saline solutions, such as a solution of sodic 
sulphate, if saturated at a high temperature and allowed to 
cool in a closed vessel, or in a flask whose neck is plugged with 
cotton wool, can be reduced to the ordinary temperature, with¬ 
out crystallization taking place in the same way as it would if 
the solution were exposed. On introducing into the solution 
when cold certain substances, some of which are always to 
be found in the air, but the nature of which has not yet 
been clearly made out, a mass of crystals is produced ex¬ 
tending throughout the solution, and the temperature rises 


46 


SOURCES OF HEAT. 


very considerably. In fact, the “ super-saturated solution/’ as 
it is called, is in a state of strain, and this strain is suddenly 
relieved when crystallization takes place, the work done by 
the crystallizing forces being represented by the heat gene¬ 
rated. Water which has been freed from air by long boiling 
may be cooled considerably below the freezing point without 
congelation, but on being disturbed a net-work of ice crystals 
is formed throughout the water and heat is produced (equi¬ 
valent to the latent heat of the water which freezes), while 
the temperature is raised to 0°C. 

Iodide of mercury, if heated, assumes a new crystal]ine 
form, and changes its colour from red to yellow. It retains this 
form when cold if it be not subjected to mechanical violence, 
but on crushing the crystals they change to the red variety 
with evolution of heat, and the change spreads gradually 
throughout the whole mass. Boiling sulphur poured into 
cold water assumes a plastic form, and can be stretched like 
India-rubber. This material gradually changes to an opaque 
crystalline mass, and heat is evolved during the transforma¬ 
tion. Sometimes the formation of each crystal in a hot 
saturated solution of salts is accompanied by a flash of light. 

Yellow phosphorus when heated nearly to its boiling 
point and maintained at this temperature for several hours 
assumes the red or amorphous condition, and much heat is 
absorbed during the operation. If this red phosphorus be 
heated too much it returns to the yellow variety with explo¬ 
sive violence, and the heat absorbed during the former trans¬ 
formation is restored. 

68. If we trace back any supply of heat as far as 
possible we find that, if we neglect such unimportant sources 
as meteors, we always arrive either at the internal heat of 
the earth, the earth’s motion of rotation converted into heat by 
the intervention of the tides and machinery driven by them, or 
the radiation from the great centre of our system, the sun. 
Take for example the heat generated in a wire, through which 
an electric current due to a zinc-carbon battery is passing. 
The heat is derived from the energy of the current, which 
is itself derived from the combination of the zinc with the 
exciting liquid. Now this energy is due to the attraction 


SOURCES OF HEAT. 


47 


of the zinc for certain components of the liquid, and for the 
energy of this attraction the zinc is indebted to the heat 
which separated it in the reducing furnace from its com¬ 
bination with oxygen, &c. in the ore. This heat is due to 
the combustion of the coal, and therefore to the attraction 
which the coal possesses for oxygen, and for this attraction 
the coal is indebted to the energy of the solar radiation, 
which, acting through the machinery of a vegetable organ¬ 
ism, separated the carbon, &c. from combination with oxygen 
at the time when the trees grew from which our coal has 
been produced. 


CHAPTER IV. 


EFFECTS OF HEAT UPON MATTER. 


69. Bodies may be divided into two classes, solids and 
fluids. 

Def. A solid is a body which requires a finite stress to 
produce a finite change in its form with or without change of 
volume. 

Def. A perfect fluid is a body whose form can be changed 
to any extent , provided its volume remain constant , by the 
application of a stress , however small , if we allow it sufficient 
time. 

One solid is said to be more rigid than another, when, 
other things being the same, it requires a greater stress to 
produce in it the same change of form. A solid would be 
perfectly rigid if no finite stress, however great, could produce 
any change whatever in its form or volume. We know of 
no body perfectly rigid or perfectly fluid. 

As illustrations we may refer to a piece of hard steel, 
which requires a very great force to produce a permanent 
impression upon it; while its own weight is sufficient to 
make any quantity of water acquire the form of the vessel 
into which it is poured. 

A body is said to be elastic when if strained it tends 
to return to its original form or volume after the constraint 
has been removed. Fluids are elastic for changes of volume 
only, and have no tendency to assume any particular shape. 
(The spheroidal form assumed by drops of liquid is due to the 


DISTINCTION BETWEEN LIQUIDS AND GASES. 


49 


combined action of gravity and a tension of the surface of 
the liquid, known as surface tension , to which reference has 
already been made in describing maximum and minimum 
thermometers. Capillary action is due to the same cause.) 

There are many substances which occupy a kind of inter¬ 
mediate position between solids and liquids,.as, for example, 
many vegetable gums, &c., and are called viscous. 

70. Fluids are divided into two classes, viz. liquids and 
gases. 

Def. A liquid is a fluid, a finite portion of which cannot 
be made to occupy more than a certain definite volume , 
however the pressure to which it is exposed may be dimin¬ 
ished. 

Def. A gas is a fluid, any finite portion of which may 
be made to occupy any space, however great, by sufficiently 
diminishing the pressure to which it is exposed. 

For example, if a cup of olive oil, or strong sulphuric 
acid, be placed under the receiver of an air-pump the liquid 
will not sensibly change its volume, however perfect a 
vacuum may be formed around it; while if a cubic inch of 
air at ordinary pressure be allowed to enter an exhausted 
receiver of any capacity, the air will expand and completely 
fill the receiver, exerting an uniform pressure all over its 
surface, as may be shewn by the same fall being produced 
in columns of mercury in manometer tubes communicating 
with the receiver at different points. This power of indefinite 
expansion is the essential characteristic of a gas. 

71. According to the molecular theory of gases now 
generally accepted, we may perhaps say proved, a gas con¬ 
sists of perfectly free particles or molecules moving in all 
directions and with different velocities but such that the 
energy due to the motion of the particles in any sensible 
mass of the gas depends only on the temperature, increasing 
with it. The motion of each particle is unaffected by any 
other particle except when very close indeed to it, when the 
particles rebound from each other like perfectly elastic balls. 
From this view of the constitution of a gas it follows that 
any finite quantity of a gas will expand into any portion of 

G. 4 


50 


COEFFICIENT OF LINEAR EXPANSION. 


space to which it has free access. The pressure exerted by 
a gas on a surface in contact with it is due to the repeated 
impact of its particles in the same way as the pressure 
exerted by a jet of water from a fire-engine is due to the 
impact of the several particles of water in the jet. The 
pressure is of course increased when the velocity is increased, 
and in the case of the fire-engine jet is proportional to the 
square of the velocity if the sectional area of the jet be 
given. So, in the case of gases, the pressure increases with 
the velocity of the particles, being proportional to the mean 
square of the velocity; it therefore increases with the tem¬ 
perature, and as we shall learn in the next chapter, is pro¬ 
portional to the temperature as recorded by the air ther¬ 
mometer, whose zero is — 273° C. 

72. We have seen that the effect of the entrance of 
heat into bodies is in general to increase their temperature, 
and this is usually accompanied by increase of volume, if the 
pressure to which they are subject be not increased so as to 
prevent it. Water between the temperatures of 0° C. and 
4° C., iodide of silver, baked clay, and one or two alloys, are, 
however, notable exceptions to this rule, since they contract 
on increase of temperature. 

Among solids the metals as a general rule expand most 
for a given increase of temperature, but ebonite expands 
much more than any metal. 

Def. The ratio of the increase in length of a bar of any 
substance , due to an increase in its temperature of 1° C., to the 
original length of the bar at 0° G., is called the coefficient of 
linear expansion of the substance. 

Thus if the length of a bar of copper is one foot at 0° C. 
and T0017 feet at 100° C., its mean coefficient of expansion 
between 0°C. and 100°C. is ’000017; for if the expansion were 
uniform between 0° C. and 100° C. its length at 1° C. would 
be T000017 feet, and the ratio of the expansion to the 
original length would then be *000017. 

73. The linear expansion of bars may be conveniently 
measured by means of the apparatus shewn in fig. 10. AB 


EXPANSION OF METALS. 


51 


Fig. 10. 



is a bath of oil or water which can be heated to any required 
temperature, and the temperature 
observed by means of a thermo- 
meter. CD is a small bar which \ 
can turn about a centre at C , and 
carries a blunt knife-edge at D 
resting against the end K of the 
bar KL, whose expansion is to be 
observed. The arm CD carries 
a small mirror near C, and the distance between the 
centre of motion C and the knife-edge at D is accu¬ 
rately known. The end L of the bar KL rests against 
a fixed obstacle, as, for instance, the end of the vessel, 
and the centre C and end of the vessel B should be 
so supported that the distance between C and L is in¬ 
variable. The adjustment should be so made that during the 
experiment the mean position of the line CD is as nearly 
as possible vertical. A ray of light is allowed to fall on the 
mirror in the direction EC , which remains constant, and is 
reflected along CF, forming a spot of light on a scale con¬ 
veniently situated. When the bar KL is heated it expands, 
and the end K pushes D before it, since L is fixed. This 
causes the arm CD, and with it the mirror, to turn about (7, 
the reflected ray CF consequently being deflected through 
twice the angle through which CD turns. This angle is 
indicated by the deflection of the spot of light on the scale, 
and hence the angle through which CD turns, and there¬ 
fore the distance through which D moves, or the linear 
expansion of LK, can be at once determined. 


This method is similar to that of Lavoisier, who em¬ 
ployed a telescope attached to the arm CD instead of the 
mirror, and through it observed a fixed scale. The mirror 
has the advantage of being much lighter than the telescope, 
and therefore more easily mounted, while it deflects the ray 
through twice the angle through which it turns. 

In order to make accurate measurements with the mirror, 
a horizontal wire should be stretched in front of the source 
of light, and a lens placed between the wire and the mirror 
so that a distinct image of the wire is thrown upon the gradu¬ 
ated scale. The scale should be circular, and have the mirror 


4—2 



52 


EFFECTS OF HEAT UPON MATTER. 


at its centre. The motion of the image of the wire will 
then at once indicate the angle through which the mirror 
is turned. 

By causing the end B of the bar to press against a micro¬ 
meter screw inserted in the end of the trough we can find 
how many turns of the screw produce the same deflection as 
the expansion of the bar when heated, and thus determine 
approximately the actual expansion. 

74. To shew the expansion of metals for purposes of 
demonstration the apparatus shewn in fig. 11 is very con- 

Eig. 11. 


i 



venient, though it cannot be used for exact measurements on 
account of the extensibility of the string by which the mirror 
is moved. The mirror instead of being directly connected 
with the lever at G is carried on a separate shaft at M. The 
pivot G is placed very near to the lower end A of the lever, 
and to the upper end of the lever a string is attached which 
passes round a small’shaft carrying the mirror and supports 
a weight at the end, or is attached to a steel spring which 
keeps it stretched. In this way the angle through which 
the mirror turns is very much increased. It is important 























MEASUREMENT OF COEFFICIENTS OF EXPANSION. 53 


that the pivot G should be rigidly fixed with respect to the 
end B of the rod, and this is ensured by the strong brackets 
shewn in the figure. The bath is supported upon pieces of 
wood fastened to the stand by hinges for the convenience of 
removing it. If the diameter of the mirror shaft at M be 
T 3 gdn., the length of GD 3 inches, that of AG Jin., and of AB 
12 inches, then if the bar be zinc, a change of temperature of 
about 64° Centigrade will turn the reflected ray through 
180°, but if the bar be iron, the same change of temperature 
will turn the ray through only 72°, shewing that the co¬ 
efficients of expansion of zinc and iron are nearly as 5 : 2. 

75. The mean coefficients of linear expansion of some 
substances between 0° C. and 100° C. are given in the fol¬ 
lowing table. 

Table of Coefficients of Linear Expansion. 


Glass tube 

about 

•000008 

Crown glass 

a 

*000009 

Platinum 

a 

•000009 

Cast iron 

a 

•000011 

Soft steel 

a 

•000011 

Steel tempered yellow 

a 

•000013 

Wrought iron 

a 

•000012 

Gold 

a 

000016 

Copper 

a 

•000017 

Brass 

a 

•000019 

Silver 

a 

•000021 

m* 


T000022 to 

I in 

a 

1000028 

Lead 

a 

•000028 

Zinc 

a 

•000030 


The coefficients of expansion of metals vary very much 
with their physical state, so that the above table must be 
taken as only approximately true. 

76. Def. The coefficient of cubic expansion of a sub¬ 
stance at any temperature is the ratio of the increment of any 
volume of the substance produced by an increase in its tem¬ 
perature of 1° G. to the original volume at 0° (7. 



54 


COEFFICIENT OF CUBIC EXPANSION. 


Most substances, except crystals, expand' equally in all 
directions when heated. Imagine a cubic block, the length 
of whose edge is 1 foot: its volume will then be 1 cubic 
foot. Now suppose that om raising its temperature 1°C. the 
length of its edge becomes 1 + a feet, so that a is its coefficient 
of linear expansion. Then its volume is 1 + 3a + 3a 2 + a 3 
cubic feet, and the increment of its volume is 3a -h 3a 2 + a 3 
cubic feet. The ratio of this to the original volume, viz. one 
cubic foot, is 3a + 3a 2 + a 3 , which expression is therefore the 
coefficient of cubic expansion. Now a is, in general, very 
small; hence a 2 and (a fortiori) a 3 may be neglected in com¬ 
parison with a. We have then for the coefficient of cubic 
expansion 3a, or the coefficient of cubic expansion is three 
times the coefficient of li/near expansion for the same sub¬ 
stance. 

In the case of copper a is about *000017. Hence 3a is 
about *000051, 3a 2 about '000000000867 and a 3 about 
'000000000000004913. It is obvious that both 3a 2 and a 3 
may be neglected without producing any sensible error in 
the result, each being far less than the limits of experi¬ 
mental error in the determination of a. 

77. The effect of neglecting the terms involving a 2 and a 3 
may be illustrated by taking a cube of 10 centimetres side, 
three plates each 10 centimetres.square and one centimetre 
thick, three strips each 10 centimetres long and one centimetre 
Fig. 12. 










EXPANSION OF LIQUIDS. 


55 


square and a cubic centimetre. Placed together these will 
build up a cube of 11 centimetres edge. If we neglect the 
three strips and the cubic centimetre our enlarged cube is 
incomplete at the edge (Fig. 12), and this is equivalent to 
neglecting 3a 2 and a 3 in the above expression. 

Or we may employ the following illustration. Take a 
cube of wood or other material of one foot edge, and let this 
represent the unit of volume. Suppose a to be 01. Then 
a piece of pasteboard of one foot square and '01 ft. thick 
will contain a units of volume, while its thickness will be a 
units of length. Take three such plates, the sum of whose 
volumes is 3a, and apply them to the three faces of the cube 
which meet in a point. Now take three rectangular strips 
of pasteboard a foot long and *01 ft. square. The volume of 
each of these is a 2 , and the volume of the three together is 3a 2 . 
If these strips be laid in the grooves formed by the edges of 
the plates, there will only be required a cube of 01 inch 
side and volume a 3 in order to complete a cube of 1*01, or 
1 + a, feet edge. The whole increment in volume of the one 
foot cube is the volume of the three plates together with that 
of the three strips and the small cube or 3a + 3a 2 +a 3 . If we 
take the coefficient of cubic expansion to be three times that 
of linear expansion, that is, take into account the plates only, 
we neglect the strips and the little cube; but even when the 
linear expansion is so great as *01 of the original length, the 
error so introduced is very little more than one per cent. 

78. Before explaining the methods of measuring directly 
the cubic expansion of solids we must consider the cubic ex¬ 
pansion of liquids, for as the volumes of irregular solids can 
only be determined from the amount of liquid which they dis¬ 
place, so we should expect that any changes in their volumes 
must be measured in the same way. The usefulness of 
liquids for this purpose depends on the property in virtue of 
which any quantity of a liquid can be made to assume the 
form of a regular prism or cylinder by pouring it into a 
vessel of that shape, and its volume can then be computed 
by measuring its linear dimensions. 

If a liquid be heated in a glass vessel, both the glass 
and the liquid expand. The apparent expansion of the 


56 


EXPANSION OF LIQUIDS. 


liquid in the vessel is due to the difference between the 
expansion of the liquid, and that of the interior of the vessel. 
There are two methods in general use for the measurement 
of this expansion. The first consists in filling with the 
liquid the bulb and part of the stem of a thermometer tube, 
the capacity of the bulb and different parts of the length of 
the stem at some particular temperature being accurately 
known. By observing the height of the liquid in the stem 
at the first temperature, the volume of liquid at that tem¬ 
perature is known. The liquid is then heated, and the 
height again observed, whence the apparent increment of 
volume can be found. 

79. In the second method a specific gravity bottle is 
usually employed. This consists of a glass bottle, into which 
a stopper, having a small hole drilled through it, is accu¬ 
rately ground. The bottle having been weighed is com¬ 
pletely filled with the liquid whose expansion is to be 
measured, .and whose temperature is known. The stopper 
is then inserted, when the excess of liquid escapes through 
the perforation, and is carefully wiped away. The bottle 
and contents are then weighed, and deducting the weight 
of the bottle from the result of this weighing, we have 
the weight of the contents. The temperature of the 
bottle and liquid is then raised, and as the liquid expands 
it escapes through the stopper, ^and is wiped off. On 
again weighing the bottle we determine the amount of 
liquid which has escaped, and the ratio of this to the 
amount remaining is the ratio of the whole increment in 
volume between the two temperatures to the original 
volume. 

80. A very simple and most useful form of the specific 
gravity bottle is the weight thermometer. This consists of 
a glass tube (fig. 13) drawn out to a fine neck, which is bent 
over so that it can be made conveniently to dip into a small 
vessel of the liquid with which it is to be filled. The tube is 
first weighed when empty, and then by alternately heating it 
so as to expel the air and cooling it with its orifice under the 
surface of the liquid, the tube is completely filled. The tube 
and its contents (care being taken that it is completely full) 
are next weighed at ordinary temperatures, then heated through 


ABSOLUTE EXPANSION OF MERCURY. 


57 


a convenient range of temperature, the liquid which is ex¬ 
pelled being allowed to escape, and finally again weighed. 

Fig. 13. 



We have then all the data for determining the apparent 
expansion of the liquid. 

Suppose, for example, that the weight of the empty tube 
was 120 grains, and that when filled with mercury at 0°C. 
it weighed 720 grains, but that after it had been heated to 
100°C., its weight was 7l0'8 grains. From these data we see 
that at 0° the tube is filled by 600 grains of mercury, while 
at 100° it holds only 590 8 grains, or, in other words, 590 8 
grains of mercury at 100° occupy the same volume of glass as 
600 grains at 0°. Hence one grain of mercury at 100° occu¬ 
pies (relative to glass) times its volume at 0° or T0157... 

times its volume at 0°. The apparent expansion for an in¬ 
crease of temperature of 100°C. is therefore '0157 of the 
original volume, and the mean coefficient of apparent expan¬ 
sion between 0°C. and 100°C. is *000157. 

81. The apparent expansion of a liquid contained in any 
envelope is equal to its absolute expansion diminished by the 
increase in the capacity of the envelope, and therefore the 
coefficient of apparent expansion is equal to the coefficient of 
absolute expansion diminished by the coefficient of expansion 
of the envelope. 

Hence if we can determine the absolute expansion of 
some particular liquid, as well as its apparent expansion in a 
glass vessel due to the same change of temperature, the dif¬ 
ference between the two will give us the expansion of the 
vessel, and then, knowing the apparent expansions of other 
liquids in the same vessel, we shall only have to add to these 

















58 


ABSOLUTE EXPANSION OF MERCURY. 


quantities the expansion of the vessel, which we have deter¬ 
mined once for all, in order to obtain the absolute expansion 
of all these liquids. The determination of the absolute ex¬ 
pansion of some particular liquid is therefore of very great 
importance, and mercury is the liquid which has been em¬ 
ployed for the purpose. 




=Qc 


82. The method by which this has Fig - 14 - 

been effected may be briefly described 
as follows:— 

Two tubes AB and CD are placed 
as nearly vertical as possible, the ends 
B and G being connected by a fine tube 
which is at right angles to the vertical 
tubes and therefore in a horizontal posi¬ 
tion. The tubes are then nearly filled 
with mercury, and AB is surrounded 
with a cylinder containing oil, not shewn in the figure, and 
which can be heated to the desired temperature. The tube 
DC is surrounded by a cylinder containing melting ice. The 
heights of the cylinders are so adjusted that the mercury in 
each tube is just visible above the top of the cylinder sur¬ 
rounding it. When the mercury in each tube has acquired 
the temperature of the surrounding bath, the heights of the 
columns AB and CD are carefully measured. Then since the 
mercury in the horizontal tube BC is in equilibrium, the 
pressure at B due to the column AB is equal to that at C 
due to the column CD. Hence the densities of the mercury 
in these two columns are inversely as their heights, and 
therefore the volume of a given quantity of mercury at the 
temperature of either column will be proportional to the 
height of the column. The ratio of the difference of the 
heights of the two columns to that of the shorter will there¬ 
fore represent the total absolute expansion of an unit of 
volume of mercury between the temperature of the ice, i.e. 
0°C., and of the oil. The coefficient of expansion for mercury 
at 0°C. is thus found to be about *000179. 


A knowledge of this coefficient is necessary to enable us 
to reduce readings of the barometer to the corresponding 
readings when the mercury in the instrument is at 0°C. 







MEASUREMENT OF CUBIC EXPANSION. 


59 


83. Having thus obtained sufficient data for determining 
the absolute expansion of different liquids, we may determine 
the cubic expansion of a solid by weighing it in a liquid at 
different temperatures, the coefficient of absolute expansion 
of the liquid being known; and this process, called the areo- 
metric method, is not unfrequently adopted. 

In the same way we may determine the coefficient of 
expansion of a liquid, if we know the coefficient of cubic 
expansion of a solid, by weighing the solid in the liquid at 
different temperatures. Matthiessen adopted this method for 
determining the coefficient of expansion of water at different 
temperatures, and some of his results are given in Art. 87. 
He first carefully measured the coefficient of linear expansion 
of a glass rod, from which he deduced (Art. 76) the coeffi¬ 
cient of cubic expansion. He then cut pieces from this rod, 
and weighed them in water at different temperatures, and 
hence deduced the expansion of the water. 

84. Another method of determining the coefficient of 
cubic expansion of a solid when the coefficient of absolute 
expansion of mercury is known is by means of the weight 
thermometer. The apparent expansion of mercury in the 
glass tube must first be determined, and from this the cubic 
expansion of the glass is deduced. A bar of the substance is 
then introduced into the tube before the neck is drawn out, 
and is supported by means of two pieces of wire twisted 
round it, and projecting in such a manner as to touch the 
glass tube only in a few points, otherwise it is impossible to 
completely fill the space between the bar and the glass with 
mercury. The volume of the bar is previously determined 
by weighing it in air and in water. The neck of the ther¬ 
mometer having been drawn out, it is weighed before and 
after it is filled with mercury. After heating the thermo¬ 
meter it is again weighed, and the difference between the 
amount of mercury expelled and that which would have been 
expelled if the thermometer had been filled with mercury 
indicates the difference between the expansion of the bar and 
that of the mercury it displaces. Hence, since the coefficient 
of expansion of mercury is known, that of the bar can be at 
once determined. 

85. All bodies, with very few exceptions, expand as 


GO 


EXPANSION OF WATER WHEN COOLING. 


their temperature rises, provided they retain the same state 
of aggregation, i.e. remain solid, liquid or gaseous throughout 
the change. Exceptions to this law are however met with in 
baked clay, stretched caoutchouc, which when heated con¬ 
tracts in the direction of its tension, iodide of silver and water 
between 0° C. and 4° C., of which the last mentioned is by far 
the most important. If a quantity of water at 0° C. be 
heated, it contracts in volume as its temperature rises till it 
reaches a temperature of nearly 4° C., when its density is a 
maximum; if heated beyond this temperature it expands, 
and at a temperature between 7° C. and 8° C. its volume is 
equal to that at 0° C. It then goes on ex¬ 
panding, its coefficient of expansion per 
degree of the mercurial thermometer in¬ 
creasing slightly as the temperature rises. 

This peculiarity of water may be exhibited 
by filling a tall cylindrical jar, AB, with 
water, say at 12° C., small thermometers 
being inserted into the liquid at A and B. 

The middle of the jar is surrounded by a 
freezing mixture. As the water in the 
neighbourhood of the freezing rhixture is 
cooled, its density increases, and it descends, causing the 
thermometer at B to indicate a rapid fall of temperature, 
while that at A is very slightly affected. This goes on till 
the thermometer at B reaches a temperature of about 4° C., 
when it will cease to fall, but the thermometer at A will now 
indicate a fall in temperature, and will continue to do so 
down to 0° C., when ice will begin to be formed at the surface. 
This is known as Hope’s experiment. 

86. We may remark here that water on freezing expands 
by nearly nine per cent, of its volume, so that the ice formed 
floats on the surface of the water. This behaviour of water is 
of immense importance in the economy of nature, for when a 
quantity of water, as, for instance, a lake, cools at the surface, 
the cold water descends, warmer water from below taking its 
place; and this goes on till the whole lake has attained a 
temperature of 4° C., after which the cold water remains at the 
surface until a layer of ice is formed there, which prevents 
the rapid cooling of the remainder of the water on account 








EXPANSION OF WATER WHEN COOLING. Cl 

of the extreme slowness with which it transmits heat. We 
consequently find that in deep lakes the water below a certain 
depth is at 4° C., however cold that at the surface may be. 
Were water to continue to contract till it froze, w 7 e should 
have the whole of the water in lakes reduced to 0° C. during a 
continuance of cold weather, and if it also contracted on 
freezing, we should get an immense quantity of ice accumu¬ 
lated at the bottom of lakes, till the w T hole lake became 
frozen; for during the summer, the water warmed by the 
suns rays would float at the top, and the ice below would 
only be affected by the small quantity of heat transmitted 
through this water, and thus the ice would increase from 
year to year, till the whole lake became frozen in the winter, 
and melted in the summer only to a very small depth. 

87. The following table shews the volume of the same 
quantity of water at different temperatures according to the 


experiments of Matthiessen. 

4° C. 1*000000 

50° C. 

1*011890 

10 

1*000271 

60 

1*016715 

15 

1*000892 

70 

1*022371 

20 

1*001814 

80 

1*028707 

30 

1*004187 

90 

1*035524 

40 

1 007654 

100 

1*043114 


88. That water expands on cooling from 4°C. to 0°C. 
may be readily shewn in the following manner. Construct a 
weight thermometer with a long capillary neck. In the first 
place, determine the coefficient of apparent expansion of 
mercury in the thermometer. Suppose it to be *000155 
while the coefficient of absolute expansion of mercury is 
known to be *000179. Then the coefficient of expansion of 

2 

the glass is *000024 or about —. that of mercury. Hence if 

the thermometer be filled ^ full of mercury, the mercury 

will expand as much as the glass, and the volume of the 
interior of the thermometer above the mercury will be abso¬ 
lutely constant whatever the temperature. If the thermo¬ 
meter be then nearly filled with water so that the free surface 
is in the capillary neck when at 4°C., the ascent of the sur- 


62 


EXPANSION OF METALS WHEN HEATED. 


face manifest on lowering the temperature must be entirely 
due to expansion of the water. 

It has been mentioned previously that India-rubber when 
stretched contracts, when heated, in the direction of its ten¬ 
sion. This may be shewn by suspending a two-pound weight 
by three or four feet of red vulcanised gas tubing and then 
blowing steam from a kettle or small boiler through the tube 
when the weight will be raised through an inch or more. It 
is essential that the tube should be in good condition. Tubes 
which have been exposed to the air for a long time refuse to 
exhibit this phenomenon and it is best to procure new tube 
for the purpose. Though the tube .contracts in the direction 
of its length it expands in other directions and the volume of 
the caoutchouc is increased. 

89. The expansion of metals when heated, and their sub¬ 
sequent contraction on cooling, have been turned to practical 
account in several of the arts. Thus boiler-plates are rivetted 
with red-hot rivets, which on cooling contract, and draw the 
plates together so tightly as to form a joint impervious to 
high-pressure steam. Again, tires for ordinary carriage- 
wheels, as well as the steel tires for the wheels of loco¬ 
motives and railway carriages, are fitted on when red-hot, 
and on cooling grip them with very great force. The same 
property of iron is utilised in the manufacture of the Arm¬ 
strong and the Fraser gun. In these guns, the breech is 
surrounded by a number of iron cylinders, made by winding 
bars into helices, and welding each turn to the next so as to 
form a cylinder in which the fibre of the iron is arranged in 
a helix about the axis of the gun. The first cylinder is turned 
so as to fit easily over the breech of the gun when the latter 
is cold but itself red-hot. It is then heated and slipped into 
its position, after which the gun is immersed in cold water. On 
cooling, the cylinder tends to contract, and exerts great pres¬ 
sure on the breech. The next cylinder is turned so as to fit 
over the first in a similar way, and so on, Armstrong guns 
sometimes having 5 or 6 cylinders placed one over the other. 
Each cylinder, except the outside one, is then subjected to an 
enormous pressure, on account of the tendency of the cylinder 
surrounding it to contract upon it, while in its turn it exerts 
pressure on the cylinder within it. Hence when the powder 


PRACTICAL APPLICATIONS. 


63 


explodes, the pressure of the gases produced has to balance 
the contractile forces of all the cylinders, before it can exert 
any force effective in producing a strain on the breech of the 
gun. Guns thus constructed will consequently bear the ex¬ 
plosion of very heavy charges without bursting; a pressure of 
about 70 tons weight per square inch being sometimes ex¬ 
erted within them. 

In several cases in which the walls of buildings have 
bulged outwards, they have been drawn together by passing 
iron bars through them across the building, heating the 
bars, and, when expanded, screwing nuts upon their pro¬ 
jecting ends. On cooling, the bars drew the walls together, 
and the process was repeated till they assumed their proper 
positions. 


90. An idea of the force which iron exerts if prevented 
from contracting when cooled from a high temperature to 
ordinary temperatures, may be gathered from the following 
rough calculation. 


Suppose an iron bar, one square inch in section, cooled 
from 500° C. (a dull red heat) to 0°C. It would, if allowed, 
contract from a length represented by r006 to a length 
represented by 1, its coefficient of expansion being about 
*000012. The bar therefore when at 0°C. is stretched beyond 


its natural length by 


6 

1000 


of that length. 


Now the force 


capable of stretching a bar of iron of 1 sq. inch section by 
this amount is about equal to the weight of 15 tons, which 
therefore represents the force with which it tends to con¬ 
tract. If heated to only 100°C. the force it exerts on 
cooling will be equal to the weight of about 13 tons, the 
elasticity of iron being very imperfect when stretched so 
much. 


91. Though the expansion of metals by heat is thus 
frequently applied to useful purposes it is perhaps more 
frequently a source of trouble. Thus in order to allow for 
expansion, the pipes of water and gas mains have to be con¬ 
nected by telescope-joints; the consecutive metals on a rail¬ 
way have to be placed at a small distance apart, the bolt¬ 
holes through which they are bolted to the fish plates being 


G4 


PRACTICAL APPLICATIONS. 


elongated, and so on. The tubular girders of the Britannia 
bridge are each mounted on rollers at the end, while the 
metals are halved together, as shewn in fig. Fig> 16# 

16, so as to allow a play of about nine ^ 

inches, without making a gap between 

them. 

The flanged iron pipes often used to convey steam from 
boilers to engines are connected by copper connecting pieces 
of the form shewn in the figure. As the pipes expand or 
contract these copper connections have their curvatures 
changed so as to accommodate themselves to the pipes. 

Fig. 16 a. 



The patterns for castings must be made somewhat larger 
than the castings required. In the case of cast iron about 
an eighth of an inch per foot is allowed for contraction in 
cooling. 

The contraction of metal castings when cooling often 
produces great strains in the metal and not unfrequently the 
castings are broken. For example, in a wheel having a thin 
rim and thick round arms and a massive boss the rim will 
solidify and cool before the arms and boss. As the arms cool 
subsequently the contraction of the arms and boss is opposed 
by the rim of the wheel, and one or more of the arms are 
often fractured. To avoid this the arms are often bent so 
that their contraction on cooling may tend to straighten 
instead of fracturing them. 

As castings are frequently broken through one portion 
cooling more slowly than another it is clear that in many 
cases, though fracture may not be produced, stresses are 
caused in the castings which may be on the point of pro¬ 
ducing fracture. If such castings are loaded so as to increase 






PRACTICAL APPLICATIONS. 


65 


these stresses ever so slightly fracture may ensue though the 
load may be far less than the computed “safe load” for the 
structure. The strains induced in glass by rapid cooling will 
be referred to in Chapter VII. 

If furnace bars are made with square ends so as to fit 
tightly in their places they are compelled to bend on account 
of the expansion they undergo when heated. For this reason 
the ends of furnace bars should be bevelled off on the lower 
side at an angle less than the limiting angle of friction and 
should be carried on bearers bevelled to the same angle, 
plenty of room being left between the ends of the bars and 
the ends of the furnace. 


92. In the construction and use of standards of length 
it is of extreme importance that the temperature should be 
carefully observed, and corrections made for expansion or 
contraction. The Imperial standard yard is defined as the 
distance between the centre of two fine lines engraved on the 
gold plugs which are inserted in a certain bronze bar kept in 
the Exchequer Chamber, and known as the Imperial stand¬ 
ard yard, the temperature of the bar being 62° F. From this 
it will be seen that before employing the bar as a standard it 
must be brought to the temperature of 62° F. The room at 
Southampton which was constructed by Col. Clarke for the 
standards belonging to the Ordnance Survey, is most care¬ 
fully protected from changes of temperature by double walls 
and double doors so arranged that the first must be closed 
before the second can be opened. 


93. In field work it is of course impossible to keep the 
measuring bars always at the same temperature, and it is 
therefore necessary to know their coefficients of expansion, 
and to observe this temperature from time to time during 
the day in order to make the necessary corrections. The 
measuring bars designed by Colonel Drummond for the 
Indian Survey are so ar¬ 
ranged, or compensated, 
that the distance between 
the marks is independent 
of the temperature. Their 
construction is illustrated 


Fig. 17. 


JJ. 




G. 






66 


PRACTICAL APPLICATIONS, 


by the diagram (fig. 17). is a bar of brass, and CD an 

equal bar of iron. These are connected by the cross pieces 
EGA , FDB by pins at A, B, G and D. The points 
which mark the ends of the standard are placed at E and F, 
so that AE : GE :: BF : DF :: coefficient of expansion of 
brass : coefficient of expansion of iron. If the temperature 
be raised AB expands more than CD, and the bars AE, BF 
are caused to incline towards one another in such a way that 
the distance between E and F remains unchanged. Micro¬ 
scopes are employed along with the bars, and one microscope 
is placed upon the ground and its moveable wire adjusted 
till it coincides with the image of E. The bar is then 
advanced, and so placed that the image of F is on the wire, 
and then the microscope is again moved to E. Two micro¬ 
scopes are generally employed to prevent accidents, and the 
first is not moved till the second is adjusted. 

94. Perhaps the expansion of metals causes more trouble 
to horologists than to any other class of persons. The rate 
of a clock is usually governed by a pendulum, and the time 
of vibration of a pendulum depends on the distance between 
the centres of suspension and of oscillation. Now, if the 
pendulum consist of a simple metallic rod carrying a weight, 
when it is heated it expands, and this distance is increased, 
so that the clock is retarded, while on cooling it is accelerated. 
A compensating pendulum is one in which the distance 
between the centres of oscillation and suspension is inde¬ 
pendent of the temperature. 

95. A compensating pendulum may be constructed on 
precisely the same principle as the Drummond bars, with 
this difference, that the cross piece BD (fig. 17) should be 
rigidly connected to the bars AB and CD, so that only AE 
may change its inclination. The centre of suspension should 
be connected to B, the bar AB being somewhat produced, 
and the pendulum bob suspended from E. For the sake of 
symmetry the arrangement may be duplicated about AB t 
so that there are bars corresponding to CD and AE on each 
side of AB. Ellicott’s pendulum is only a modification of 
this, the iron bar being placed between two brass bars, and 


graham’s mercurial pendulum. 


67 


a ring attached to the lower end of the iron bar, which is 
pivoted to two cross pieces, from the outside extremities of 
which the hob is suspended. The brass bars press upon the 
other extremities of the cross pieoes and thus by their ex¬ 
pansion raise the points of suspension of the bob. 

96. In Graham’s mercurial pendulum the bob consists 
of a glass vessel containing mercury. Now the coefficient of 
apparent expansion of mercury in glass is very much greater 
than the coefficient of linear expansion of the iron suspension- 
rod, and while the latter expands downwards, the centre of 
gravity of the mercury in the glass vessel is raised by the 
expansion of the mercury, and the quantity of mercury is so 
arranged that the latter expansion just compensates for the 
former, and the centre of oscillation remains unmoved. 
The rod of Graham’s pendulum was made of glass, but 
mercurial pendulums are now usually constructed with iron 
rods. 

97. Harrison’s gridiron pendulum is shewn in fig. 18. 
The vertical rods there indicated by black lines yig. 18. 
consist of iron, those shewn by light lines, of 
which only four are shewn in the figure though 
there should be at least six, are made of brass. It 
is obvious from the construction that the expan¬ 
sion of the iron rods, which are supported at 
their upper ends, tends to lower the bob, while 
that of the brass rods, all of which are sup¬ 
ported at their lower ends, tends to raise it. Since 
the coefficient of expansion of brass is, roughly 
speaking, about 1J times that of iron, it fol¬ 
lows that the ratios of the lengths of the brass 
bars to those of the iron bars, and the distri¬ 
bution of metal throughout the pendulum, can 
be so arranged as to keep the distance between 
the centres of suspension and oscillation inde¬ 
pendent of the temperature. 

98. A form of pendulum which is much more easily con¬ 
structed than the gridiron pendulum and answers better, 

5—2 












68 


COMPENSATING PENDULUMS. 


inasmuch as it exposes less surface to the friction of the 
air, and has its centre of mass much lower Fig. 19. 
down, is shewn in fig. 19. It consists of an 
iron tube, AB, shewn in section in the 
figure; inside this tube and fitting it loosely 
is placed a zinc tube which is supported by 
being rivetted to the iron at B. From the 
top of the zinc tube hangs an iron rod, CD, 
which carries the bob. Here it is obvious 
that the pendulum will be compensated if 
2 

BG be about equal to’ ^ (AB + CD), since 



the coefficient of linear expansion of zinc is 
about 2J times that of ironi In order to 
give sufficient length to the zinc tube, these 
pendulums are usually constructed so that 
the point B is within a< hole drilled 1 through 
the bob. 


UZX _J 


99. The movements of watches- and chronometers are 
governed by “ balance-wheels ” which oscillate under the 
action of the elasticity of the hair-spring, to which they 
are attached. The time of oscillation of the wheel de¬ 
pends upon its moment of inertia, 
and increases with it. Now this 
is increased by increasing the dia¬ 
meter of the wheel, though the 
mass remains unchanged. Hence 
a simple balance-wheel will cause 
the rate of the watch to diminish 
as the temperature increases. This 
is obviated in the chronometer 
balance-wheel shewn in fig. 20, by 
making the circumference of the 
wheel of two metals, the outer of 
which is some metal, as brass, 
whose coefficient of expansion is great, while the inner metal 
is steel, or some other, whose coefficient of expansion is 
small. The circumference is cut into two or three parts, 
each of which is supported at one end by an arm of the 


Fig. 20. 













CHRONOMETER BALANCE. 


GO 


wheel.. Now, if the temperature increase, the distances of 
the points A, B, C from the centre of the wheel will increase 
on account of the expansion of the arms, while the curva¬ 
ture of the arcs AD, BE, CF will increase because the outer 
metal will expand more than the inner. This will occasion 
the points D, E, F to approach the centre, and the weights 
of the heavy screws attached to each arc can be so adjusted 
that the moment of inertia, and therefore the time of oscil¬ 
lation, of the wheel is unaffected by change of temperature. 
Balance-wheels are generally made by first turning a small 
wheel in steel and then casting a ring of brass around it 
before cutting through the circumference. 


100. The change of curvature produced in a compound 
bar, similar to the circumference Fig 21 

of the balance-wheel, by change . _ 3 

of temperature, may be shewn 
by rivetting together at an or¬ 
dinary temperature plane strips _ 

of zinc and brass, or of silver 483 

and platinum, as in fig. 21, where 
the brass is shaded. On heating 

the strip it will assume the - 

second form shewn, while on 
cooling it in a freezing mixture it will take the third form. 
This experiment shews conspicuously the difference in the ex¬ 
pansion of two metals for the same increments of temperature. 


101. Breguet’s thermometer consists of very thin strips 
of silver, gold, and platinum, which are rolled together so 
as to form a thin narrow ribbon, and this is wound into a 
helix in which the silver is on the outside and the platinum 
on the inside. If the temperature of the ribbon increase, 
the helix winds itself tighter because the expansion of the 
outside is greater than that of its inner surface, while, when 
it is cooled, it partially unwinds. If one end of the ribbon 
be fixed, and a needle or mirror attached to the other end, a 
very sensitive thermometer is obtained. 

This thermometer is sometimes employed as a rough 
galvanometer for indicating the passage of an electric cur- 











70 


breguet’s thermometer. 


rent. The helix is supported at the top by a metal arm 
connected with one electrode, while a wire connected with 
its lower end dips into a cup of mercury in communication 
with the other electrode-. The current thus flows through 
the helix itself and manifests its presence- by its heating 
effect. 

102. The points upon railways are connected with the 
pointsman’s, lever by iron rods, and when the distance is con¬ 
siderable the expansion and contraction of the rods through 
changes of temperature would cause the points to move 
without any change in the position of the lever if no pre¬ 
caution were taken to prevent it. In order to overcome 
this difficulty the connecting rods are fastened to short fevers 
BCD, EFG (fig. 22), which can turn freely about pivots C , 
F, which are fixed relative to the permanent way. If A 

Fig. 22- 


?. 7I % === M 

1 * K _ffi 

jy . 

represent the end of the rod which is attached to the fever, 
and H the end which is connected with the points, the con¬ 
dition that H should remain fixed as long as A is fixed is 
that the expansion of BE should be equal to that of AB 
and GH together, or that the length of DE should be equal 
to the sum of the lengths of AB and GH. Any number of 
fevers similar to BCD may be introduced, but the condition 
which must always be fulfilled by the bars is that the sums 
of the lengths of the alternate bars should be the same. 








CHAPTER V. 


ON THE EFFECTS OF HEAT UPON GASES. THE GASEOUS LAWS. 

COOLING OF GASES BY EXPANSION. SPECIFIC HEAT OF AIR 

AT CONSTANT PRESSURE AND AT CONSTANT VOLUME. 

DIFFUSION OF GASES. 

103. We have now to consider the effects of heat upon 
gases. A gas has been defined as a fluid , a finite portion 
of which can be made to occupy any assigned space' however 
great , by sufficiently diminishing the pressure to which it is 
exposed. In speaking then of the volume of a quantity of 
gas, it is of primary importance to specify the pressure under 
which this volume is measured. The law connecting the 
volume and pressure of a given mass of gas at constant tem¬ 
perature is known as Boyle’s, or Mariotte’s, law, and is as 
follows:— 

The volume of a given mass of gas at constant tempera¬ 
ture varies inversely as its pressure ; or, The product of the 
numerical measures of the volume and pressure of a given 
mass of gas at constant temperature is constant. 

104. This may be shewn experiment¬ 
ally by partially filling a tall U tube, 

ABC, with mercury, closing the end C, 
and then pouring mercury into, or out of, 
the arm AB. It will be found that when 
the air in BC has acquired its original 
temperature after this operation, its vo¬ 
lume will vary inversely as the sum or 
difference of the height of the mercu¬ 
rial barometer and of the difference in 


Fig. 23. 


M c 


KJ' 

B 






72 


EXPANSION OF AIR. 


height of the surfaces of the mercury in the two arms of the 
tube, that is, inversely as the whole pressure to which it is 
subjected; the difference of level of the mercury in the arms 
being added to the height of the barometer when the mer¬ 
cury in AB stands above that in BG, and subtracted from it 
when the opposite is the case. 

105. Instead of the U tube a more convenient appara¬ 
tus consists of two glass tubes connected by a few feet of 
flexible indiarubber tubing, having a small bore and thick 
wall so as to be able to sustain a pressure of six or eight feet 
or more of mercury. The tube which corresponds to the 
arm G in Fig. 23, and which should be of uniform bore or 
be calibrated, is fixed to a long vertical scale while the tube 
corresponding to the arm A can be moved up and down the 
scale. The two tubes being placed at the same height mer¬ 
cury is poured into the apparatus till it reaches the middle 
of the tubes. The tube A should then be raised till G is 
completely filled with mercury. The upper end of G which 
has been left open should then be connected with a desic¬ 
cating apparatus so that on lowering A pure dry air may be 
drawn into G, and when G is about one-third full of air its 
upper end should be sealed with the blow-pipe flame. The 
pressure upon the air in G may then be increased or dimin¬ 
ished to any extent within the limits fixed by the length of 
the India-rubber tube, while the difference in level of the 
surfaces of the mercury in the tubes is measured by the 
scale. By employing a scale etched on plate glass and sil¬ 
vered at the back, all danger of parallax can be removed by 
causing the surface of the mercury to exactly cover its 
image formed in the mirror-scale. This last device is due 
to Professor Jolly. 

106. The increase in volume of a quantity of air for a 
given change of temperature, when the pressure is kept con¬ 
stant, may be roughly determined by taking an empty ther¬ 
mometer tube, warming it, and, 
when it begins to cool, dipping 
the end under the surface of 
mercury for a very short time, 
so that a small pellet of mercury 


Fig. 24. 




EXPANSION OF AIR. 


73 


may be made to enter the tube. The volume of the air 
within the instrument will then be determined by the posi¬ 
tion of the pellet of mercury. This apparatus will serve as an 
air thermometer for a small range of temperature. By heating 
the bulb in a bath, whose temperature is measured by a 
mercurial thermometer, it will be found that the volume of 
the air increases very nearly uniformly for equal increments 
of temperature indicated by the mercurial thermometer. 

107. If the thermometer be filled with any other gas, 
which cannot be readily liquefied, as Oxygen, Hydrogen, 
Nitrogen, &c., it will be found that the coefficient of expansion 
is almost precisely the same as for dry air, and that for every 
increase in temperature of 1° C., under any constant pressure, 

each of these gases expands by about of the volume it 

would have at 0° C. under the same pressure (though this 
rate is not quite uniform if the temperature be indicated 
by the mercurial thermometer). If the volumes of quan¬ 
tities of these different gases, always subject to the same 
pressure, be equal at some particular temperature, they 
will also be almost exactly equal when they are all at any 
other, the same, temperature. Hence, thermometers filled 
with any of the so-called permanent gases all indicate the 
same scale of temperature , which, however, as stated in 
Chapter I., differs very little from that of the mercurial 
thermometer. 


108. From the preceding we see that, if v 0 represent the 
volume of any quantity of a permanent gas at 0° C., and 
v t its volume under the same pressure at t° C., then 



Thus if the gas occupied 273 cubic inches at 0° C., it would 
occupy 274 cubic inches at 1° C., and 373 cubic inches at 

100° C. The fraction —^ is often denoted by a. 


109. Now suppose that instead of having the air in a 
bulb tube we have it in a tube of uniform bore throughout 


74 


THE AIR THERMOMETER. 


and closed at the lower end. Then the volume of the air 
will be proportional to the distance of the bottom of the 
pellet of mercury from the bottom of the tube. Suppose 
that when the temperature is 0° C. the air occupies 27‘3 
inches of the tube. Let a mark be placed at this distance 
from the bottom, and called the freezing point. Now place 
the whole tube in the steam above boiling water, as in the 
case of the mercurial thermometer described in Chapter I.; 
it will then be found that the air will occupy 373 inches 
of the tube. Marking the tube at this height, (calling it 
the boiling point,) and dividing the distance between this 
point and the freezing point into 100 equal parts, or degrees, 
each degree will occupy one-tenth of an inch of the tube. 
Marking off distances each equal to the tenth of an inch 
below the freezing point, and indicating them by the cor¬ 
responding number with a negative sign prefixed, we find 
that the bottom of the tube is marked — 273°. Hence we 
infer that if the law of contraction of air with decrease 
of temperature remained the same as at ordinary tempera¬ 
tures, and we could cool the air to a temperature corre¬ 
sponding to - 273° C., its volume would be zero. Of course 
we never expect to realise this, for*even supposing it possible 
to attain this low temperature, which we never hope to do, 
the air would probably cease to be a gas long before reach¬ 
ing it. The temperature corresponding to the bottom of the 
tube is called the absolute zero of the air thermometer, and 
temperatures reckoned from this point are called absolute 
temperatures. The absolute temperature of the freezing 
point is therefore 273°, and that of the boiling point 373°. 
Now the volume of the air in the tube at any temperature 
is proportional to the length of the tube which it occupies, 
and therefore to the absolute temperature indicated by its 
upper surface. Hence we see that, 

The volume of any mass of air, or other gas, at constant 
pressure increases uniformly with the temperature , and is 
proportional to the temperature reckoned from the absolute 
zero of the air thermometer. 

This is sometimes called Charles’, but more generally 
Gay Lussac’s, law. Boyle’s law and this together constitute 
“ the gaseous laws,” which should be carefully remembered. 


PRESSURE OF GAS AT CONSTANT VOLUME. 


to 


110. Ex. A quantity of gas occupies 10 cubic inches 
at a temperature of 15° G.; what will be its volume under the 
same pressure at 75° GJ 

15°C. corresponds to (273 + 15)°, or 288° above the abso¬ 
lute zero of the air thermometer, while 75°C. corresponds to 
an absolute temperature of 348°. 

At 288° Abs. Temp, the gas occupies 10 cubic inches. 


at 1° 

.*. at 348° ... 


it would occupy cub. ins. 


10 x 348 
288 


cub. ins. 


= 1208...cub. ins. 


This is perhaps the simplest method of finding the rela¬ 
tive volumes of a quantity of gas, corresponding to different 
temperatures. 


111. Boyle’s law states that the product of the numerical 
measures of the pressure and volume of a given mass of gas 
remains constant while the temperature remains so, and we 
have just seen that if the pressure be kept constant the 
volume is proportional to the absolute temperature. 

Now let v denote the volume, and p the pressure of a 
quantity of gas whose temperature, reckoned from absolute 
zero, is T°. Let the temperature be changed to T" the 
pressure remaining the same. Let the volume then become 
v x . Then 

T 

^1 ^ ~rji .(- 0 * 

T 

and pv l =pv-^. 

Now let the pressure be increased, the temperature re¬ 
maining at T* till the volume is again reduced to v, and 
let p l denote the pressure when this is the case. Then since 
the temperature is kept constant, 

p 1 v=pv 1 , by Boyle’s law, 




76 


PRESSURE OF GAS AT CONSTANT VOLUME. 


V. 

=?§l>y (1). 

Now if the gas were heated to T its volume being kept 
constant, we should finally have arrived at the same state of 
things as by the process we have adopted, and the pressure 
would then, as now, be denoted by p v Hence, 

The pressure of any mass of gas whose volume is kept 
constant increases uniformly with the temperature , and is 
proportional to the temperature reckoned from the absolute 
zero of the air thermometer. 

Fig. 25. 

112. This result may be tested 
experimentally by an apparatus de¬ 
signed by Professor Balfour Stewart, 
the essential portions of whidh are 
shewn in fig. 25. 

AB is a vessel containing mer- k 
cury and closed at one end by a 
piston which can be made to slide 
in and out through a stuffing box 
by means of the screw S ’, and thus 
to change the capacity of the vessel 
AB. E is a vertical glass tube com¬ 
municating with the interior of AB, 
and open at the top, while the tube F is connected with 
a very fine tube leading from the glass bulb K. The bulb K 
is filled with perfectly dry air, and then attached to F. K 
is then cooled to some known temperature, as by placing it 
in a quantity of melting ice, and the mercury in F is made 
to rise to a marked point G , where the tube is very narrow, 
by turning the screw S. The excess of the height of the 
mercury in the open tube E over its height in F, when 
added to the height of the barometer, gives the whole pres¬ 
sure to which the air in K is subjected. Call this P. The 
bulb K is then heated to some known temperature, as, for 
instance, by placing it in the steam over boiling water, and 


lr cD— U ■ 

A JB £ 











RELATION BETWEEN PRESSURE, VOLUME, & TEMPERATURE. 77 


the piston C is advanced by means of the screw S till the 
mercury in F again reaches G. Determining as before the 
pressure to which the air in K is subjected, and denoting 
it by P v we find that 

T 

P = P 1 

x i x rji > 


where T° and Tf denote the temperatures of the bulb in the 
first and second experiments respectively, reckoned from 
the zero of the air thermometer. If the temperatures em¬ 
ployed are those of melting ice and of the steam over water 
boiling at the standard pressure, we find 


P = 



The cylinder and piston, which is necessarily a somewhat 
expensive apparatus, may be replaced by a strong vessel of 
India-rubber which can be slowly compressed between two 
plates of metal by means of a screw. 


113. Professor Jolly’s air thermometer, which serves 
the same purpose as the last mentioned instrument, is similar 
to the apparatus described in Art. 105, except that the tube 
G is replaced by a bulb tube so bent that it can be conve¬ 
niently raised to any desired temperature in a bath and 
having a portion of its neck, in which the surface of the 
mercury is kept, very narrow. The bulb tube is-also sup¬ 
plied with a branch and stop-cock through which it can be 
exhausted and filled with any gas which may be desired. 

114. We have seen then, that, if the pressure be kept 
constant, the volume of a given mass of gas varies as its 
absolute temperature, while if the volume be kept constant 
the pressure varies as the absolute temperature. Hence, 
when both volume and pressure are allowed to vary 
together, 

The product of the numerical measures of the pressure and 
volume of a given mass of gas increases uniformly with the 
temperature, and is proportional to the temperature reckoned 
from the absolute zero of the air thermometer . 


78 


THE GASEOUS LAWS. 


115. As an example of the application of the preceding 
laws we may take the following:— 

A quantity of air occupies 1 cubic foot at a temperature 
of 59° F. and under a pressure of 30‘24 inches of mercury. 
It is required to find its volume at 113° A under a pressure 
of 28*62 inches of mercury . 


59° F. corresponds to 15° C. or an absolute temperature 
of 288°, while 113° F. corresponds to 45° C. or 318° C. above 
the absolute zero of the air thermometer. Hence if the 
pressure remained constant the volume at 113° F. would he 


ix S cub - feet - 


But the pressure changes from 30*24 to 28*62 inches of 
mercury, and the volume varies inversely as the pressure. 
Therefore the actual volume is 


318 
288 X 


i^cub. ft. = Ucub. ft. 


Or we may proceed thus:— 

Volume at 288° under pressure of 30*24 inches is 1 e. ft. 


1 ° 


.. 30*24 
. 1 


288 °* ft ‘ 


30*24 

288 


c. ft. 


.*.318° 


28*62 

28*62 


' 288 x 28'62 C ' ft ' 
-20-24 x 318 
’ "288x28-62 ° At 


116. We have seen that if the volume he kept constant, 
the pressure of a given mass of gas is proportional to its 
temperature above the absolute zero of the air thermometer. 
Hence at the absolute zero of temperature, the pressure of 
any quantity of gas would be zero, supposing the same law 
to hold at such a low temperature. Now, according to the 
molecular theory of gases, a gas consists of a number of very 













EXPANSION OF GASES. 


79 


small particles, or molecules, moving about with great velocity 
in all directions (Art. 71). The pressure of the gas on any 
surface in contact with it is due to the continual impacts of 
these molecules; and it may be shewn that the pressure of a 
gas upon a surface is proportional to the kinetic energy, or 
vis-viva, possessed by the unit of volume of the gas. Hence, 
when this pressure is zero, it follows that the gas possesses 
no kinetic energy, and that its particles are therefore at rest. 
This is a reason why the zero of the air thermometer should 
be considered to be the absolute zero of temperature. 

117. A perfect gas is an ideal substance which strictly 
follows Boyle’s law. All known gases deviate to some extent 
from this law, and those which deviate most from Boyle’s 
law also deviate most from Gay Lussac’s law. Gases which 
can be readily liquefied deviate considerably from the gaseous 
laws and the more so as they approach the temperature and 
pressure at which they become liquid; when the coefficient of 
expansion rapidly increases. 

As a general rule gases have a greater coefficient of ex¬ 
pansion than liquids, and liquids than solids. The coeffi¬ 
cients of expansion of liquids and solids generally increase 
as the temperature is raised, if the temperature be measured 
by the air thermometer. 

118. In the following table the second column contains 
the mean coefficients of expansion of the gases mentioned in 


Name of gas. 

Constant 

pressure. 

Constant 

volume. 

Hydrogen 

•003661 

•003667 

Air 

•003670 

•003665 

Nitrogen 


•003668 

Carbonic oxide 

•003669 • 

•003667 

„ anhydride 

•003710 

•003688 

Nitrous oxide 

•003719 

•003676 

Sulphurous anhydride 

•003903 

•003845 

Cyanogen 

•003877 

•003829 







80 


DIFFERENTIAL THERMOMETER. 


the first column between 0° C. and 100° C. at constant ordi¬ 
nary pressure, and the third column indicates the mean 
rate of increase of pressure of the same gases for the same 
range of temperature when the volume is constant. The 
numbers are due to Regnault. 

119. From the table given in the last Article it will 
be seen that the coefficients for hydrogen, nitrogen, and 
carbonic oxide, gases which can be liquefied only by means 
of intense cold and pressure, are sensibly the same as for 
air, while in the case of each of these gases the rate of 
increase of volume per degree of temperature, when the 
pressure is constant, is very nearly the same as the rate 
of increase of pressure when the volume is constant, or the 
gases obey Boyle’s law. The coefficients of expansion of the 
other gases mentioned in the table differ sensibly from that 
of air, and in their cases the rates of increase of volume and 
of pressure are not the same, that is, the gases diverge 
sensibly from Boyle’s law. These gases can be liquefied with 
comparative ease. 

As mentioned in Chapter I., it is the almost exact agree¬ 
ment between the expansions of air, hydrogen, oxygen, nitro¬ 
gen, carbonic oxide, and some other gases at different tempe¬ 
ratures which renders the scale of the air thermometer of 
peculiar importance, and moreover the specific heat of these 
gases is the same at all temperatures measured by the air 
thermometer. 

120. The great coefficient of expansion of air renders it 
useful for the construction of sensitive ther¬ 
mometers. A common form of the differential 
thermometer is shewn in fig. 26. It consists 
of a glass tube bent as shewn in the figure, 
and having a bulb at each extremity. The 
middle portion of the tube is partly filled 
with coloured liquid, while the two upper 
bends are united by a short tube which can be 
closed by a plug tap, A. When A is opened 
the pressures in the two bulbs are equalised, 
and the liquid stands at the same height in ( 
each limb. The tap A is then closed. Now ^ 









HEAT PRODUCED BY COMPRESSION. 


81 


if the temperature of the bulbs be initially the same, and if 
the temperature of either, or both, change, the pressure of 
the air will be greater in that whose temperature suffers the 
greater increase, and the liquid will be driven by the excess 
of pressure towards the other bulb, the difference of the 
heights at which it stands in the two limbs roughly indicat¬ 
ing the difference in the changes of temperature of the two 
bulbs. If the bulbs differ in temperature when A is closed, 
the liquid will remain undisturbed provided the absolute 
temperature of each be increased by a quantity proportional 
to itself. 

Leslie’s differential thermometer was somewhat simpler 
than that just described, the tube being bent only twice at 
right angles, and a bulb being placed at the top of each 
branch of the tube. 

121. If a quantity of air be confined in a cylinder into 
which a piston is accurately fitted, and the piston be sud¬ 
denly and violently depressed so as to compress the air, the 
latter will be considerably heated; so much so, that German 
tinder placed within the cylinder may be ignited, or if a 
glass cylinder be used, and a little vapour of bisulphide of 
carbon diffused through the air within it, the vapour may 
be inflamed, producing a brilliant flash. 

122. Suppose a quantity of air heated from T° to T°, 
its volume remaining constant. Its pressure will be cor¬ 
respondingly increased. Now let the air expand until its 
pressure is the same as before; during this operation the air 
will become cooled and heat will have to be communicated 
to it in order to restore it to the temperature of Tfi Sup¬ 
pose, on the other hand, that the air is heated, its pressure 
being kept constant; then when the air reaches the tem¬ 
perature of T* it will be precisely in the same condition as 
if its temperature had been raised from T 0 to T x ° in a closed 
vessel so that its volume was kept constant. We thus see 
that the amount of heat required to raise the temperature 
of the air from T° to T* under constant pressure, is greater 
than the amount required to produce the same rise of tem¬ 
perature w T hen its volume is constant, by the amount of 
heat given out by the air during the third of the above 
operations. From this experiment we learn that the specific 


82 


AIR EXPANDING INTO VACUUM. 


heat of air at constant pressure is greater than its specific 
heat at constant volume. (Dr Joule shewed that the differ¬ 
ence was almost equivalent to the work done by the air in 
expanding.) If both the pressure and volume were allowed 
to increase the specific heat would be intermediate between 
these two, while if the volume increased so much that the 
pressure diminished, it would be greater than the first; and 
if the pressure increased so much that the volume di¬ 
minished, it would be less than the second. 

123. Since gases become heated when suddenly com¬ 
pressed, it will follow that, if allowed to expand, by relieving 
the pressure, the gases will be cooled, provided they do not 
receive heat from without. We shall meet with instances of 
this in a subsequent Chapter. 

124. If a quantity of gas be allowed to expand without- 
doing any external work, as when it expands into a vacuum, 
no heat is lost or gained by the gas as a whole. This was 
shewn by Dr Joule, who connected a vessel containing com¬ 
pressed air, at a pressure of about 22 atmospheres, with a 
second vessel which was exhausted, the communication be¬ 
tween them being closed by a tap. * The two vessels were 
placed under the water in a calorimeter, and after they had 
acquired the temperature of the water, the tap was opened. 
The temperature of the water remained unaffected. Hence 
when air expands without doing external work, no heat is 
lost or gained by it. The air left in the first vessel did work 
in driving the air into the second with great velocity, and 
was itself cooled, but the air entering the second vessel 
on striking against its sides acquired as much heat by the 
impact as was lost by that in the first, so that as much heat 
was communicated to the water by one vessel as was taken 
from it by the other. 

125. In Art. 48 we explained how the specific heats of 
air, and other gases, at constant pressure, were determined 
by Kegnault. The results of his investigations may be 
summed up in the following laws. 

1. The specific heat of a permanent gas at constant 
pressure is independent of that pressure , and the same for all 
temperatures. 


REGNAULTS PYROMETER. 


83 


2. The capacity for heat of EQUAL volumes of different 
permanent gases at the same pressure and temperature are 
equal. 

3. The specific heats of the easily condensible gases vary 
slightly with the temperature. 

The experimental determination of the specific heat of 
air at constant volume is one of extreme difficulty. An 
indirect method by which this has been effected will be 
described in Chapter X. We may, however, here remark 
that, for all the more perfect gases, the ratio of the spe¬ 
cific heat at constant pressure to that at constant volume 
is independent of the temperature of the gas, and for air is 
about 1*41. 

126. It has been stated, Art. 106, that the scale of the 
mercurial thermometer differs but very slightly from that of 
the air thermometer. In the course of his experiments on 
the maximum pressure of aqueous vapours at different 
temperatures, Regnault made a series of comparisons be¬ 
tween the readings of his mercurial thermometer, with an 
envelope of crown glass, and those of an air thermometer. 
Some of his results are given in the following table. Below 
100° C. the readings were practically the same. 


Thermometer. 

Mercury Thermometer. 

100° C. 

100° C. 

140 

139'85 

180 

179-63 

200 

199-70 

240 

239-90 

260 

260-20 

300 

301-08 

340 

34300 

350 

354-00 


127. The expansion of gases has been turned to practical 
account in the construction of pyrometers, or instruments 
for measuring very high temperatures, as of furnaces. Of 
these Regnault’s mercury pyrometer may be taken as an 
example. It consists of a bottle of iron, or porcelain, 

6—2 


84 


regnault’s pyrometer. 


the neck of which has a narrow opening, and is covered 
by a lid whose diameter is considerably greater than its 
own. The lid has a small hole bored through it, and the 
top of the neck and lower surface of the lid are ground 
together, so that by sliding the lid on the neck the bottle 
may be opened or closed. A small quantity of mercury is 
placed in the bottle, and the whole placed in the furnace. 
The quantity of mercury must be sufficient to expel, when 
volatilised, all the air from the bottle, and when it has ac¬ 
quired the temperature of the furnace the neck is closed 
by sliding the cover, and the instrument removed and al¬ 
lowed to cool. When cold the mercury within it is weighed, 
and this gives the weight of mercury vapour which filled 
the bottle at the temperature of the furnace. The capacity 
of the bottle is determined by weighing it when full of 
mercury, and weighing it when empty. Then if w r e know 
the height of the barometer, and the specific * gravity of 
mercury and of mercury vapour at any temperature and 
pressure, as well as the law of expansion of mercury vapour, 
we can calculate the temperature of the furnace. 


128. Suppose for example that the amount of liquid 
mercury at 15° C. required to fill the bottle is 314 ozs., and 
that at this temperature a cubic foot of mercury weighs 
13564*8 ozs. Then it follows that the capacity of the flask 
is 40 cubic inches. Suppose also that the amount of mer¬ 
cury left in the bottle after being removed from the furnace 
is 13 grains, and that at 360° C. a cubic foot of mercury 
vapour weighs 1580 grains, when under the same pressure 
as during the experiment. Then if the temperature of the 
furnace be T° C. 40 cubic inches of mercury vapour will 
weigh 

1KQ , 40 360 + 273 . 

1580 X 1728 X T + 273 S rams - 


supposing mercury vapour to behave as a perfect gas at tem¬ 
peratures above 360° C. But 


1580 x 


40 „ 360 + 273 
1728 X r+273 





WEDGWOOD’S PYROMETER. 


85 


therefore 


therefore 


T+ 273 = 


1580 x 40 x (860 + 273) 
1728 x13 


= 1780*87... 
T= 1507*87... 


and the temperature of the furnace is nearly 1508° C. 


129. In Wedgwood’s pyrometer the temperature is mea¬ 
sured by the contraction of a piece of baked clay; others 
have been constructed in which the temperature is indicated 
by the expansion of a platinum bar. The action of Siemens’ 
pyrometer depends upon the increase of the resistance which 
platinum wire offers to the passage of an electric current as 
its temperature is raised. It consists of a very fine platinum 
wire wound on a small porcelain bobbin, the ends of the 
wire being attached to very thick wires whose resistance is 
exceedingly small compared with its own. The bobbin is 
placed within the furnace, with the thick wires leading from 
it to any convenient place, and the resistance of the wire is 
then measured in the usual way, and the temperature of the 
furnace deduced. 


Diffusion of Gases. 

130. If two vessels containing different gases be allowed 
to communicate with each other for some time, it will be 
found that each vessel contains a mixture of the gases of 
the same composition, and this will be the case even if 
one of the gases be much denser than the other, and the 
vessel containing it be placed at a considerable distance 
below that containing the lighter gas, the communication 
being made by a tube. Oxygen may be used for the heavier, 
and hydrogen for the lighter gas, and the mixtures subse¬ 
quently exploded. 

This phenomenon is known as the diffusion of gases , and 
in virtue of it the atmosphere has nearly the same com¬ 
position at all heights to which men have ascended. It is 
sometimes expressed by saying that one gas acts as a vacuum 
to another. 



86 


DIFFUSION OF GASES. 


131. If, in accordance with the molecular theory of 
gases, we suppose that a gas consists of a number of very 
small particles moving in all directions with great velocities, 
we see that they will penetrate into any space which is open 
to them, and the presence of any other gas in that space will 
only delay their diffusion through it by causing them to 
continually come into collision with its own particles, just as 
the passage of a person through a crowd is impeded by the 
presence of others, and would be much more so were all 
the persons composing the crowd, and including the intruder, 
highly elastic and perfectly devoid of intelligence. The 
molecular theory of gases thus readily accounts for the 
phenomenon of diffusion, and we see that either gas will 
ultimately be uniformly distributed throughout each vessel, 
because it is only then that the number of its particles pass¬ 
ing from the first to the second vessel in any given time will 
be equal to the number passing in the opposite direction. 

The molecular theory of gases also teaches us that at the 
same temperature the mean squares of the velocities of the par¬ 
ticles of different gases under any given pressure vary inversely 
as the density of the gas, and this accounts for the law dis¬ 
covered by Graham, that gases diffuse into one another at 
rates varying inversely as the square roots of their densities. 

132. The differences in the rates of diffusion of different 
gases have been employed to detect the presence of coal-gas 
or fire-damp. An instrument for this purpose known as 
Ansell’s fire-damp indicator consists of a small balloon made 
of thin India-rubber and inflated with air. A linen band 
placed round its equator necessitates any expansion it may 
undergo taking place in the direction of its vertical diameter. 
An alarum is so placed that if the balloon, which is fixed 
into a suitable frame, expand vertically it will by raising a 
detent start the alarum. If the apparatus be placed in an 
atmosphere containing hydrogen or carburetted hydrogen 
more gas will enter the balloon by diffusion through the 
envelope than will leave it, because at first it contains only 
pure air, and both oxygen and nitrogen are more dense than 
hydrogen or carburetted hydrogen. The contents of the 
balloon being increased the envelope will expand vertically 
and liberate the alarum. 


CHAPTER VI. 


ON THE EFFECTS OF HEAT IN PRODUCING CHANGES OF STATE 
IN BODIES. LATENT HEAT. REGELATION. EVAPORATION. 
BOILING. DEW-POINT. CRITICAL POINT. SPHEROIDAL 
STATE. 

133. If heat be made to enter a solid body its tempera¬ 
ture will, in general, be increased, and the solid will expand, 
until it arrives at a certain temperature (which depends for 
each solid only on the pressure to which it is subjected) 
called the fusing point, when the solid will begin to liquefy, 
and the temperature will remain unchanged till the whole 
of the solid is converted into the liquid state. During this 
process the volumes of most bodies increase, but there are 
many substances which, like ice, cast iron, and many alloys, 
contract on fusing and expand during solidification, and this 
enables sharp castings to be taken in these materials. 

134. During the process of liquefaction the application 
of heat has to be continued, and a large amount is absorbed 
by the melting body. This heat has no effect upon the tem¬ 
perature of the body, which, as we have said, remains con¬ 
stant till the whole is liquid. On this account the heat 
absorbed during this process was said to become latent , and 
was called the latent heat of fusion. It may be thus de¬ 
fined:— 

Def. The latent heat of f usion of a substance is the 
number of units of heat absorbed by the unit of mass of the 
substance in passing from the solid to the liquid state without 
change of temperature. 


88 CONTRACTION ACCOMPANYING SOLIDIFICATION. 


In Chapter III. we saw that a pound of ice in melting at 
0° C. would cool a pound of water from 79° C. to 0° C. The 
latent heat of fusion of ice, or, as it is more generally called, 
the latent heat of water, is therefore 79. 

135. The phrase “latent heat” is not well chosen, be¬ 
cause the heat absorbed during liquefaction does not remain 
within the substance as hidden heat, or heat insensible to 
the thermometer, but actually ceases to be heat, being used 
up in doing internal work; just as when a steam crane is 
employed in lifting building stones, part of the heat gene¬ 
rated in the furnace ceases to be heat, being used up in 
doing work, and having its representative in so many tons of 
material lifted so many feet against the attraction of the 
earth. 


136. There are some substances which, like ice and 
cast iron, expand on solidification. The density of ice at 0° C. 
is *918, that of water at 4° C. being taken as the standard of 
density, but as its temperature is lowered the ice contracts, 
its coefficient of cubic expansion per 1°C. being about *000122. 
Those metals which expand on solidifying are well adapted 
for making sharp castings, since on solidification they expand 
and fill all the interstices of the mould. On the other hand, 
it is impossible to obtain sharp castings with metals like 
gold, silver, lead, &c. For this reason coins, medals, rifle- 
bullets, &c. are stamped. When a leaden bullet is cast there 
is always an empty space inside it, due to the contraction of 
the lead, and the resultant resistance of the air then not 
generally acting through the centre of gravity of the bullet 
its direction of motion is thereby changed. It is to obviate 
such action that a motion of rotation is given 
to bullets and cannon-shot by rifling the guns, 
but in addition to this rifle bullets are always 
punched out of cold lead instead of being cast. 

Paraffin contracts very much on solidifying, and 
if a cylindrical vessel be filled with melted pa¬ 
raffin and allowed to cool, the upper surface of 
the paraffin will be depressed in the centre, as 
shewn in Fig. 27, while castings made in closed moulds will 
generally be found interspersed with cavities. 


Fig. 27. 





REGELATION. 


89 


187. It \gis first shewn from theoretical considerations 
by Prof. James, Thomson, that if a body expand on solidifi¬ 
cation an increase of pressure will lower the melting point, 
but if it contract on solidifying, like wax and paraffin, the 
melting point will be raised by pressure. Sir W. Thomson 
subsequently found that in the case of ice the melting point 
is lowered by about for each additional pressure of one 

atmosphere. This dependence of the melting point upon the 
pressure explains the phenomenon of regelation. 

An example of this phenomenon is presented by the 
following experiment. A block of ice is supported in any 
convenient manner at each end, and a wire loop carrying 
a weight is suspended from the block, the temperature of 
the air being above the freezing point. The ice immediately 
underneath the wire being then exposed to a pressure greater 
than that of the atmosphere, while its temperature is not 
sensibly below the freezing point, melts, and the liquid so 
formed escaping to the upper side of the wire where the 
pressure is only that of the air, while the temperature of the 
water is below the freezing point, it again freezes. (That the 
temperature of the water must be below the freezing point 
is obvious, for in melting it must absorb the necessary latent 
heat from the surrounding ice, cooling it below the freezing 
point, and it is this cooling which prevents the wire from 
cutting through the ice instantly, for the cooled ice is able 
to support the pressure of the wire, and the rate at which 
the cutting goes on is determined by the rate at which the 
heat absorbed from the ice below the wire can be again com¬ 
municated to it as the water freezes above the wire.) Since, 
with the exception of a little which escapes at the edges, all 
the water again freezes above the wire, as the block is cut 
through it becomes re-united, and when the wire has passed 
completely through it the only trace left of its passage is 
a shallow groove surrounding the block, due to the escape of 
water from the surface, and a striated appearance within the 
ice along the plane of section. 

If a number of wires of the same diameter but different 
material be hung over the same rectangular block of ice and 
loaded with equal weights, it will be found that the wires 
will pass through the ice in the order of their thermal con- 


90 


REGELATION. 


ductivities. Thus if wires of copper, brass and iron be 
employed they will cut through the block in the order in 
which they have just been mentioned. 

138. Blocks of ice floating even in warm water will 
freeze together at points where they strike each other, for 
the statical pressure produced by the blow (gentle as it may 
be) is sufficiently great to lower the freezing point consider¬ 
ably and therefore to melt the ice in the immediate neigh¬ 
bourhood, when some of the water escaping with its latent 
heat the rest immediately freezes on the pressure being 
relieved. In the same way pieces of ice may be compressed 
in a boxwood mould by hydraulic pressure, and on relieving 
the pressure a transparent block is obtained of the form of 
the mould. The binding of snow when just at the freezing 
point may be due to the same cause. If the temperature of 
the ice be much below the freezing point very great pressure 
is required to melt it, and this may account for the difficulty 
of making snow-balls when the snow is “ frozen.” 


139. If a bar of wood or any other material be bent, 
one side of it is compressed while the opposite side is ex¬ 
tended. If an attempt be made to bend a bar of ice, the 
temperature of which is the freezing point, wherever there 
is pressure the ice will be partially melted, the consequent 
contraction at once relieving the pressure and allowing the 
ice to be deformed, while the conduction of heat through the 
block tends to keep the temperature the same throughout, 
and the water gradually finds its way to parts where the 
pressure is less. In the case of a bar subjected to bending 
stress, when the portion which is most compressed begins to 
melt the greatest pressure is thrown upon the next layer, 
causing it to melt and accommodate the stress, and so on 
through the block. The production of any considerable 
flexure will of course take a long time, depending as it does 
to some extent on the passage of heat through the mass, but 
it is plain that if the temperature be exactly the freezing 
point for atmospheric pressure, a stress, however small, will 
continue to produce change of form so long as it acts, and 
the ice will therefore behave like a very viscous fluid instead 
of a solid. 


EEGELATION. 


91 


What has just been stated will go far to explain the 
motion of glaciers, but in their case fracture of the ice no 
doubt frequently occurs in passing round a bend, but on 
coming to a bend in the opposite direction the crevasses 
thus formed are closed and the pressure causes the surfaces 
to melt while part of the water escapes, and then regelation 
takes place, completely healing the wound and obliterating 
its traces. 

140. As a general rule, if a liquid be cooled to the melt¬ 
ing point the process of cooling cannot be carried further 
without solidification taking place, but water may be cooled 
considerably below the freezing point if it be carefully freed 
from air by long boiling and the surface be protected by a 
film of oil. In capillary tubes water has been cooled b} 7- 
Despretz to — 20° C. without solidifying. When water has 
been cooled in this way, if it be disturbed so that solidifica¬ 
tion commences, a net-work of ice crystals is suddenly formed 
throughout the mass and the temperature rises to 0°C. A 
similar action takes place in the case of certain saline solu¬ 
tions, such as that of sulphate of soda (Art. 67), which may 
be cooled without crystallizing, though at the lower tempera¬ 
ture they contain much more salt in solution than can be 
dissolved by water at that temperature. On disturbing such 
solutions a mass of crystals is quickly formed, extending com¬ 
pletely through the liquid, while the temperature rises on 
account of the production of heat by crystallization (latent 
heat of solution). 

The laws of fusion may be thus stated :— 

1. Each substance begins to melt at a certain tempera¬ 
ture, which is constant for the same substance if the pressure 
be constant, and is called the melting point 

2. The temperature of the solid remains constant from 
the time when fusion commences until it is complete. 

3. If a substance expand on solidifying, e.g., ice, its 
melting point is lowered by pressure; but if it contract, e.g., 
wax, its melting point is raised by pressure. 

4. The unit mass of each substance in passing from 


92 


EVAPORATION. 


the solid to the liquid condition without change of temperature , 
absorbs a certain quantity of heat which is constant for the 
same body melting at the same pressure and temperature , and 
is called the latent heat of fusion. 

141. Most liquids and some solids when exposed to the 
air pass gradually into the gaseous state. The process by 
which liquids and solids assume the gaseous condition at 
their free surfaces is called evaporation , and the gas so 
formed is frequently called a vapour. It is not easy to dis¬ 
tinguish satisfactorily between vapours and gases, but the 
term vapour is generally employed for a substance in the 
gaseous condition which can exist as a liquid or solid at 
ordinary pressures and temperatures. This is the popular 
use of the terms, but the true distinction between a vapour 
and a gas lies in the fact that a vapour can be condensed to 
a liquid by the application of pressure alone, while a gas 
cannot be condensed to a liquid by the application of any 
pressure unless its temperature is reduced. There is there¬ 
fore a particular temperature above which a substance must 
be a gas, but below which it may be a vapour or a liquid 
according to the pressure v This temperature is called the 
critical point for the particular substance and will be referred 
to again shortly. The ordinary temperature of the air is far 
above the critical points of the more perfect gases. In the 
case of a liquid the converse of evaporation or the passage of 
a substance from the gaseous to the liquid condition is called 
condensation. When a gas passes directly into the condition 
of a solid it is said to sublime, and the process is called subli¬ 
mation. A solid or liquid which passes readily into the 
gaseous condition is said to be volatile. 

142. The evaporation of water is a phenomenon which 
is continually coming under our notice, and the production 
of-liquid water by the condensation of aqueous vapour is 
scarcely less familiar to us. Sometimes during a long frost 
a quantity of snow is observed slowly to vanish though the 
temperature may never rise to the freezing point, so that the 
production of liquid water is impossible: the snow in fact 
presents us with a case of the direct evaporation of a solid. 


dalton’s law. 


93 


When hoar-frost is produced by the condensation of aqueous 
vapour upon surfaces cooled below the freezing point, we 
have an example of sublimation. Solid carbonic anhydride, 
camphor, iodine, and arsenic readily evaporate without lique¬ 
faction and sublime upon colder surfaces. Flowers of sulphur 
are formed by the condensation of sulphur vapour in a large 
cold chamber. Arsenic, carbonic anhydride, and some other 
substances can be obtained in the liquid condition only 
when subjected to pressures considerably above that of the 
atmosphere. 

143. If a quantity of water or other volatile liquid be 
placed in a closed vessel, evaporation will take place until 
the pressure due to the vapour alone attains a certain limit, 
which depends only upon the temperature. The quantity of 
vapour in the enclosure will then cease to increase, though 
we do not say that evaporation will cease, but rather that 
condensation will take place at the same rate as evaporation, 
and hence the amount of vapour will remain constant. The 
quantity of vapour which could exist under given conditions 
in a limited space was for a long while a matter of enquiry, 
and Dalton was the first clearly to enunciate and verify 
experimentally the laws of evaporation. Dalton found that 
the greatest amount of vapour which can exist in a given 
space depends only upon the temperature , and is independent 
of the presence of any other vapour or gas which has no 
chemical affinity for it Regnault has shewn that this law 
is not strictly true, but it is sufficiently accurate for all the 
requirements of meteorology and volumetric analysis. It is 
sometimes expressed by saying that gases and vapours act 
towards one another as vacua . 


144. Dalton’s law may be easily verified experimentally 
by a method differing but slightly from that adopted by 
Dalton. The apparatus is represented in Fig. 28, a#d 
consists of three barometer tubes with suitable supports, , a 
mercury-bath about 3 feet deep nearly filled with mercury, 
and a scale or cathetometer for measuring the height of 
the mercury in the tubes. A yard of inch wrought-iron gas¬ 
tubing with a cap screwed to the lower end, and a cast-iron 


94 


DALTON’S LAW. 


or wrought-iron bason screwed to the upper 
end constitutes a convenient mercury-bath. 

One of the tubes, A, is filled with mercury 
and then placed vertically with its lower 
end beneath the surface of the mercury in 
the bath. This serves as a standard baro¬ 
meter for purposes of comparison. The 
tube B is filled and supported in the same 
manner, while C is only partially filled with 
mercury, so that when inserted in the bath 
such a quantity of (dry) air occupies the 
tube as to cause the mercury to stand at 
about one half the height of the barometer. 

The position of the surface of the mercury 
in C should be carefully marked on the side 
of the tube. Now let such a quantity of 
ether be introduced by means of a pipe into 
the tubes B and G , that a little of the 
liquid remains on the surface of the mer¬ 
cury. If the temperature be 15° C. the 
column of mercury will be depressed below 
that in the standard barometer by about 
354 millimetres, and if the tube B be slowly 
lowered into the mercury-bath the mercury 
will rise in the tube, the ether vapour being 
condensed, but the surface of the mercury 
will always remain 354 millimetres below 
that in the standard barometer till the whole of the vapour 
is condensed and the tube completely filled with mercury and 
liquid ether. On again slowly raising the tube the ether 
will evaporate, the surface of the mercury remaining at the 
same height as before, below that in th'e standard tube A. 
If the tube be lowered rapidly the condensation of the ether 
vapour will cause a rise in the temperature, and the pressure 
of the vapour will be increased. If the tube be rapidly 
raised the pressure of the vapour will be diminished through 
the cold caused by evaporation. 

On the introduction of the ether into the tube G the 
mercury will be seen to fall, but not so far as in B } because 
as the mercury falls the air in the tube expands and its 
pressure is consequently diminished. Now let the tube G 


















PRESSURE OF AQUEOUS VAPOUR. 95 

be lowered in the bath until the mercury rises to the point 
marked on the tube, and the air consequently occupies the 
same volume and exerts the same pressure as before. It 
will then be found that the tube has been lowered through 
354 millimetres, or the mercury in the tube stands at a lower 
level than before the introduction of the ether by 354 milli¬ 
metres, and since the pressure of the air is unchanged it 
follows that the ether vapour must exert a pressure equiva¬ 
lent to 354 millimetres of mercury, and therefore exerts the 
same pressure in the presence of the air as in the tube B 
which contains no air. 

145. If a little alcohol be introduced into the tube B 
it will immediately absorb some of the ether vapour and 
cause the mercury to rise on account of the great affinity 
which alcohol possesses for ether. Bisulphide of carbon and 
many other liquids act similarly, shewing that the pressure 
of the vapour produced by a mixture of two liquids which 
dissolve one another may be less than that of their more 
volatile component. 

For rough purposes it is convenient to close the upper 
ends of the barometer tubes by two glass taps a small dis¬ 
tance apart, or to attach to them a short piece of India-rubber 
tube with two pinch taps upon it, a small funnel being placed 
at the top. This arrangement enables the tubes to be filled 
with mercury by pressing them down into the bath till the 
mercury rises above the upper tap, the taps being open, and 
then raising them with the taps closed. By pouring the 
ether into the funnel and then opening first the upper tap 
and subsequently, after closing this, the lower tap, a small 
quantity of ether can be passed into the tube. 

146. Dalton, Gay Lussac, and, afterwards, Kegnault 
measured the pressure of aqueous vapour in the presence 
of water at temperatures below 100° C. by the depression 
of the mercury in barometer tubes as above described, the 
experimental tube being surrounded by a bath of hot 
water by which its temperature could be adjusted, while 
the mercury was observed through the glass front of the 
bath and corrections made for the expansion of the mercury 
itself. For very low temperatures Gay Lussac bent the top 


96 


WOLLASTON’S CRYOPHORUS. 


of his tube so as to incline it downwards and dipped the 
end into a freezing mixture, since the pressure of the vapour 
must always be that due to the temperature of the coldest 
part of the tube to which it has access. Kegnault followed 
the same method, and some of his results are given in the 
Table in Art. 167. 

147. The fact that the pressure of aqueous vapour in 
■ any space must be that due to the coldest part of the space 
to which the vapour has access explains the process of dis¬ 
tillation. If two vessels A and B, of which A contains a 
volatile liquid, be connected by a tube, and A be maintained 
at a temperature above that of B, the vapour in B will be 
condensed until its pressure is not greater than that due to 
the temperature of B, while evaporation will go on in A so 
long as the pressure of the vapour there is less than that due 
to its temperature; moreover, vapour will pass from A to B if 
the pressure of the vapour in A be greater than in B (though 
if the vessels contain air or other gas the diffusion of the 
vapour will be a slow process). Hence, evaporation will go 
on in A and condensation in B so long as the temperature 
of A is higher than that of B. 

148. Wollaston’s cryophorus consists of two glass bulbs 
connected by a tube and containing sufficient water to about 
half fill one bulb. The water is boiled to expel all the air 
before the tube is finally sealed, and when this has been 
done the sealing is effected with a blow-pipe flame. If the 
water be turned into the bulb A, and B be placed in a 
freezing mixture of ice and salt, condensation will take place 
so rapidly in B and evaporation in A that, on account of the 
heat absorbed in the latter process, the water in A will be¬ 
come completely frozen. 

149. As its temperature rises the pressure which a va¬ 
pour in contact with its liquid is capable of exerting goes on 
increasing, while the density of the vapour itself increases in 
consequence of increased evaporation. If a liquid be exposed 
to the open air while its temperature is gradually raised, the 
pressure which the vapour can exert will at length exceed 
that of the air, and then if a bubble of pure vapour be formed 


EBULLITION. 


97 


within the liquid itself it will rise to the free surface and 
then escape, since the pressure to which it is exposed is in¬ 
sufficient to condense it. When bubbles of pure vapour are 
formed within the liquid itself the liquid is said to boil. 
This may happen as soon as the temperature has risen so far 
that the pressure which the vapour can exert exceeds at¬ 
mospheric pressure. 

Def. The temperature at which the pressure which can be v 
exerted by a vapour in the presence of its liquid is equal to 
that of the standard atmosphere is called the boiling point of 
the liquid. 

150. The difference, then, between evaporation and ebul¬ 
lition or boiling consists in this, that in evaporation vapour is 
formed only at the free surface of the liquid, while in ebul¬ 
lition bubbles of vapour are formed within the liquid itself. 

151. When a kettle is being heated the w T ater next the 
bottom first reaches the boiling point, and bubbles of steam 
are formed there. These rising through the liquid reach a 
stratum where the temperature is insufficient to allow the 
steam to exist at the temperature to which it is exposed, and 
the bubbles contract with a sharp sound. These sounds hap¬ 
pening with sufficient frequency link themselves into a 
musical note producing the singing of the kettle. This sound 
gets feebler as the bubbles contract less sharply, and is 
presently exchanged for the smooth rolling sound of ebul¬ 
lition as the bubbles at length escape from the free surface. 

152. When a liquid boils, so long as the pressure to 
which it is exposed remains the same the temperature of 
the vapour immediately above the surface remains constant, 
though the temperature of the liquid itself may be somewhat 
different from that of the vapour. The presence of salts in 
water raises the temperature of the water, and this tempera¬ 
ture moreover depends on the nature of the containing vessel. 
Hence in determining the boiling points on thermometers 
they are immersed in the steam and not in the water itself. 
(Art. 13.) 

153. It was stated in Article 149 that if a bubble of 
vapour be formed within a mass of liquid whose temperature 

7 


G. 


98 


BOILING POINT. 


is above the boiling point, and the liquid be subjected to 
atmospheric pressure, the bubble will not be condensed, but 
it does not follow that such bubbles will be formed immedi¬ 
ately after the boiling point is reached. If water be very 
carefully freed from air by boiling, it is possible to heat it 
considerably above the boiling point without the formation 
of bubbles of steam, on account of the resistance offered by 
the water to any breach in the continuity of its mass, such as 
would be produced by the formation of steam bubbles within 
it. The boiling by bumping which often takes place with 
water, and especially with strong alkaline solutions, is due to 
this superheating of the water and the consequent genera¬ 
tion of a large quantity of steam suddenly. The introduction 
of a piece of metal which can decompose water invariably 
sets free steam with explosive violence, and the temperature 
falls nearly to the boiling point. The presence of oil on the 
surface of the water favours the superheating; and Dufour, 
by suspending drops of water in a mixture of linseed oil and 
oil of cloves, succeeded in raising their temperature to about 
180°C. without ebullition, though the pressure of steam in 
the presence of water at that temperature is equal to nearly 
ten times the standard atmosphere. It is so difficult to re¬ 
move the last trace of dissolved air and other gases from 
water, that it has been said that the phenomenon of pure 
water boiling has not yet been witnessed. 

154. Since the temperature of steam above the surface 
of boiling water depends only on the pressure, it follows that 
if we can determine the temperature of steam above the sur¬ 
face of boiling water at any place, we may find, by reference 
to tables constructed for the purpose, the barometric pressure 
to which it is subjected. The hypsometer described in Art. 12 
enables us to do this, and may therefore be employed instead 
of a barometer for the determination of the heights of moun¬ 
tains. It is from its employment for this purpose that the 
instrument derives its name. 

155. We have said that the temperature at which a 
liquid boils depends upon the pressure to which it is exposed, 
and have defined the boiling point of a liquid as that tem¬ 
perature at which the pressure of its vapour is equal to the 


EBULLITION UNDER DIMINISHED PRESSURE. 


99 


atmospheric pressure. If the temperature of the liquid be 
higher than this, vapour may be generated within its mass, 
and the liquid will then boil. If the vessel containing 
the liquid be open, the boiling will continue as long as there 
is any liquid present at a temperature above that at which it 
can boil under the atmospheric pressure, but if the liquid 
be in a closed vessel its own vapour will increase the pressure 
upon it, and presently the boiling will cease provided the 
temperature be kept constant. 

If there be no air, or gas other than the vapour of the 
liquid, above its surface, the whole pressure on the free 
surface of the liquid is due to the pressure of its vapour, and 
the amount of vapour in the unit of volume will therefore 
be that which is capable of exerting this pressure at the 
temperature of the enclosure. Since the pressure under 
which liquids boil increases very rapidly with the tempera¬ 
ture, much more so than the pressure of a given mass of 
vapour at constant volume, it follows that the density of 
the vapour above the surface of the liquid will increase 
rapidly with the temperature. 

156. If a quantity of warm water at a temperature con¬ 
siderably below 100° C. be placed under the receiver of an 
air-pump, and the air rapidly removed, the water will boil 
violently, shewing that the temperature at which water boils 
is lowered by diminution of pressure. 

The same may also be shewn in a striking manner by 
boiling a quantity of water in a glass flask until the air 
above it has been expelled by the steam, corking the neck 
of the flask, and pouring a stream of cold water over it. 
The water in the flask will then be seen to boil vigorously. 
In this case, the steam in the upper part of the flask is 
cooled much more than the mass of water below it. Its 
temperature is therefore reduced below the boiling point 
corresponding to its pressure, and part of the steam is con¬ 
sequently condensed. On account of this, the pressure on 
the surface of the water is diminished, but the temperature 
of the water is, for some time, only slightly lowered by the 
stream outside, hence its temperature is sensibly above the 
boiling point corresponding to the pressure on its surface. 

7—2 


100 PRESSURE OF VAPOUR IN THE PRESENCE OF AIR. 

The water therefore boils violently, the steam produced 
being in its turn condensed; and this process can be carried 
on for a considerable time. 

157. Now suppose that a quantity of liquid is placed in 
a closed vessel, and that there is dry air above its surface. 
Suppose also that the temperature of the water is sensibly 
above the boiling point corresponding to the pressure of the 
air above it, and is kept constant. The liquid will then boil 
violently until the pressure on its surface is equal to the 
maximum pressure of vapour at the temperature which the 
liquid possesses. When this stage is reached, the pressure on 
the liquid is the sum of the pressures exerted by the air and 
by its own vapour, and the greater the pressure of the air 
the less will be the amount of vapour per unit volume when 
the liquid just ceases to boil. 

It is found however by experiment that the formation of 
vapour in a closed vessel, when air, or any gas other than 
the vapour, is present, does not stop when the liquid ceases 
to boil, but goes on until the pressure exerted by the vapour 
alone is the maximum pressure which it can exert at the tem¬ 
perature of the liquid. During this process no bubbles of 
vapour are formed in the liquid, as is the case during boiling, 
but the vapour appears to be quietly formed at the surface, 
that is, by evaporation. 

158. Thus, in accordance with Dalton’s law, a liquid will 
go on evaporating till the pressure of its vapour alone reaches 
a certain value depending only on the temperature , and in¬ 
dependent of the presence of any amount of other vapours, 
or gases, in the same space. If a quantity of water be placed 
in a closed vessel with dry air above it, though the pressure 
of the air may be far too great to allow of the water boiling, 
nevertheless vapour will be formed till the amount above the 
water is the same as if no air had been present, the only 
difference being that in the case we have supposed the whole 
of the vapour is produced by slow evaporation , while if the 
water had been placed in vacuo its formation would have 
been much more rapid and accompanied with ebullition. We 
also see that the pressure on the water will finally exceed 
that exerted by the air, however great this may be, by a 
quantity depending only on the temperature as above stated. 


RATE OF EVAPORATION. 


101 


This is sometimes expressed by saying that different gases 
and vapours act towards one another as vacua. 

159. The rate at which evaporation appears to take 
place depends upon the temperature of the liquid and the 
rate at which vapour can escape from the neighbourhood of 
the surface’; hence movements of the air increase the ap¬ 
parent rate of evaporation. According to Dalton, the rate at 
which water evaporates in calm air at ordinary pressure is 
proportional to the difference between the maximum pressure 
of vapour at the temperature of the water and that of the 
vapour existing in the air. 

The apparent rate of evaporation is really the difference 
between the rates at which particles leave the liquid and 
become gas and that at which particles of gas enter, and 
remain within, the liquid, that is, the difference between the 
rates at which evaporation and condensation take place. 

160. If a quantity of liquid be placed in a closed vessel 
and gradually heated above the boiling point the pressure of 
the vapour will increase and exceed the atmospheric pressure. 
The pressure maybe measured by causing the vessel to com¬ 
municate with any convenient pressure-gauge, as, for example, 
an ordinary manometer or U tube containing mercury, one of 
whose arms is open to the air, while the other communicates 
with the vessel. The difference in the level of the mercury 
in the two tubes indicates the excess of the pressure of the 
vapour over that of the air. If the pressures are very great 
a continuous syphon-gauge may be employed, consisting of a 
number of U tubes connected together and half filled with 
mercury, while the spaces between the mercury in consecu¬ 
tive tubes are filled with water or other nearly incompres¬ 
sible fluid. The sum of the differences in level of the surfaces 
of the mercury in the arms of each tube, added to the height of 
the barometer and diminished by the column of mercury 
which is balanced by the water or other liquid, indicates the 
pressure of the vapour. 

161. Since it is generally impossible to raise the tem¬ 
perature of water above that at which it boils under the 
pressure to which it is exposed, in order to raise it to high 


102 


DEW-POINT. 


temperatures it must be confined in a closed vessel. Papin’s 
digester is a strong vessel (furnished with a safety-valve), in 
which water can be raised to a temperature considerably 
above 100° C., for the purpose of dissolving gelatine from 
bones, &c. On high mountains water boils at a temperature 
so low as seriously to interfere with culinary operations. 
Thus on the top of Mont Blanc the temperature of water 
boiling in the air is not much above 82° C. 

Sometimes it is of importance to cause liquids to boil at 
temperatures below their ordinary boiling points, and for 
this purpose it is necessary to reduce the pressure to which 
they are exposed below the ordinary atmospheric pressure. 
The introduction of the vacuum pan in the refining of sugar 
enabling the syrup to boil at about 66° C., allowed the process 
to be carried on without the production of the large amount 
of uncrystallizable sugar which always took place when the 
boiling was conducted at a higher temperature. 

162 . Def. When the amount of any vapour in a space 
is the greatest that can exist in it without increase of tem¬ 
perature , the space is said to be saturated with the vapour. 

Def. The temperature at which the air is saturated with 
the aqueous vapour it contains is called its Dew-point. 

If the temperature of a quantity of air containing an 
amount of aqueous vapour insufficient to saturate it be 
lowered, the air will at length become saturated, and the 
corresponding temperature is the dew-point. On still further 
lowering the temperature, condensation of part of the vapour 
takes place and the air remains saturated. 

163. From what has been said it will be seen that air 
in the presence of water must contain a quantity of aqueous 
vapour, and thus all the air around us contains more or less 
vapour, some of which will be condensed if the air be suffi¬ 
ciently cooled, condensation commencing when the dew¬ 
point is reached. 

If we have a table giving us the pressure of aqueous 
vapour for different temperatures in a space saturated with 
it, or, what is the same thing, the boiling point of water 
corresponding to different pressures, the determination of 


DEW-POINT INSTRUMENTS. 


103 


the amount of aqueous vapour in any volume of air may 
be reduced to a determination of the dew-point. The de¬ 
termination of this point is therefore a matter of considerable 
importance, and several instruments have been constructed 
for the purpose. 

164. A simple form of dew-point instrument, introduced 
by Mr Dine, consists of a metal box covered with a piece of 
polished black glass, a thermometer being placed with its 
bulb in close contact with the glass. A stream of cold water, 
whose rate can be regulated at pleasure, is made to flow 
through the box, and when a film of moisture begins to 
render dull the polished surface of the glass, the stream is 
stopped and the thermometer read. In a few seconds the 
cloud will begin to leave the glass, and the thermometer is 
again observed. The mean of the two temperatures is 
approximately the dew-point. 

165. DanielPs dew-point instrument, frequently called 
Daniell’s hygrometer, is shewn in Fig. 29. A bulb A made 
of black glass is connected with the 
bulb C by the tube ABC, of clear 
glass. The bulb A contains a quan¬ 
tity of liquid ether, into which dips 
the bulb of a small thermometer T. 

The whole apparatus is exhausted 
of air before being sealed, so that 
the bulbs contain only ether and 
its vapour. The bulb C is covered 
with muslin or similar material, and 
when the instrument is to be used 
liquid ether is poured over the mus¬ 
lin. This evaporates, and in so doing 
absorbs the latent heat of evapora¬ 
tion (see Art. 170), cooling the bulb 
and allowing the ether vapour within it to condense, thus 
diminishing the pressure within the tube. This causes the 
ether in A to evaporate with a consequent lowering of the 
temperature of A, and after some time moisture begins to be 
deposited on the outside of the bulb. The thermometer T 
is then observed and the muslin on C is allowed to become 














104 


WET AND DRY BULB THERMOMETERS. 


dry. The temperature of A will then gradually rise, and 
when the dew upon it begins to disappear, the temperature 
of T is again observed. The mean of the two readings of T 
is taken as the dew-point. 

Regnault’s dew-point instrument consists of two test tubes 
silvered at the bottom. In one of these ether is placed and 
air blown gently through it until the evaporation has lowered 
the temperature so that dew begins to be deposited on the 
silver cap. The second tube is merely for purposes of com¬ 
parison, in order the more readily to detect the first appear¬ 
ance of dew on the former tube. A thermometer is placed 
with its bulb in the ether. 

166. Mason’s dry and wet bulb thermometers, some¬ 
times called August’s psychrometer, are frequently used for 
determining the amount of moisture in the air. They con¬ 
sist of two thermometers mounted side by side, the bulb of 
one being exposed while that of the other is covered with 
lamp-cotton, or muslin, kept wet by dipping one end into a 
vessel of water, when the water rises in the cotton, as spirit 
in the wick of a lamp, and the bulb of the thermometer is 
thus kept wet. Now if the air be far from saturated with 
moisture, the water will evaporate rapidly from the cotton, 
and in doing so will cool the bulb of the thermometer below 
the temperature of the air, the amount of such cooling being 
less the more nearly the air is saturated. Empirical formulae, 
based on the assumption that evaporation continues until 
the air is saturated at the temperature to which it is reduced, 
have been employed for the determination of the dew-point 
from the temperatures indicated by the thermometers, and if 
the current of air to which the instrument is exposed be 
gentle, the method admits of considerable accuracy. 

The determination of the dew-point, or of the amount 
of moisture in the air, is called hygrometry, and instruments 
employed for this purpose are called hygrometers, or Dew¬ 
point instruments, as the case may be. 

It should be noticed that in all practical determinations 
of the dew-point the air in the neighbourhood of the dew¬ 
point instrument is cooled at constant 'pressure. Its volume, 
therefore, diminishes during the cooling, and the volume of 


HYGROMETRY. 


105 


the aqueous vapour is correspondingly diminished. Since 
both air and vapour obey the gaseous laws it follows that, 
since the sum of their pressures remains constant, the pres¬ 
sure of the vapour alone will remain constant up to the point 
when it begins to condense, that is the dew-point. The 
maximum pressure of aqueous vapour at the dew-point as 
ordinarily determined is therefore the same as the actual 
pressure of the vapour in the air, and no correction for tempe¬ 
rature is required. 

167. When the temperature of a quantity of vapour is 
above the dew-point so that the space is not saturated with 
it, the vapour is sometimes said to be super-heated. Reg- 
nault has shewn that aqueous vapour at temperatures between 
0°C. and 25°C., obeys the gaseous laws with considerable 
accuracy provided it is not on the point of condensing. 

Table of Pressure of Aqueous Vapour. 


Temperature. 

Pressure. 

Temperature. 

Pressure. 

- 32° C. 

Millimetres. 

0-320 

90° C. 

Millimetres. 

525-450 

-20 

0927 

100 

760-000 

-10 

2-093 

110 

1075-37 

-5 

3-113 

120 

1491-28 

0 

4-600 

130 

2030-28 

5 

6-534 

140 

2717-63 

10 

9-165 

150 

3581-23 

15 

12 699 

160 

4651-62 

20 

17-391 

170 

5961-66 

30 

31-548 

180 

7546-39 

40 

54-906 

190 

9442-70 

50 

91*982 

200 

11688-96 

60 

148-791 

210 

14324-80 

70 

233-093 

220 

17390-36 

80 

354-643 

230 

20926-40 


Hence if we know the dew-point and the temperature of the 
air, and are moreover furnished with a table shewing the 
maximum pressure of aqueous vapour at different tempera- 






106 


HYGROMETRY. 


tures, we can determine the amount of aqueous vapour exist¬ 
ing in a cubic foot of air. Balfour Stewart has proposed to 
measure the degree of humidity of the air by the ratio of the 
amount of vapour actually existing in it to that which would 
be required to saturate it at the temperature it possesses. 
Tables have been constructed by Regnault giving the maxi¬ 
mum pressure of aqueous vapour for every tenth of a degree 
Centigrade near ordinary temperatures, and then for every 
degree up to 230° C. A few of his results are given in the 
preceding Table, the pressures being expressed in millimetres 
of mercury at 0° C. in the latitude of Paris, and 60 metres 
above the sea level. 

168. As an example illustrating the subject of hygro- 
metry we may take the following:— 

Find the weight of dry air in a cubic foot of air con¬ 
taining aqueous vapour at 15° G. under a pressure of 30 
inches of mercury , when the dew-point is 10° G., it being given 
that a cubic foot of dry air at 0° G. and under the above 
pressure weighs 554 grains, and that the pressure of aqueous 
vapour in a space saturated with it at 10° G. is equal to the 
pressure of '36 in. of mercury. 

The amount of aqueous vapour in the cubic foot is such 
that at 10° C. it would exert a pressure equal to that of 
•36 in. of mercury. The pressure exerted by the dry air 
occupying the same volume is therefore equal to that of 
30 — *36 in. of mercury, = 29'64 in. of mercury. Hence the 
volume which the dry air would occupy under a pressure of 

oq.fu 

30 inches of mercury at 15° C. is OA cub. ft., and the 

o(J 

volume it would occupy at 0° C. under the same pressure 
. 29-64 273 2964 

1S 3Q x 288 CU ^' ^ an( * we ^ t is therefore 554 x — 

273 

x— grams, 

= 521*12 grains, nearly. 

169. The fact that the amount of aqueous vapour capable 
of existing in a cubic foot, or other definite amount, of space 
above the surface of water is independent of the presence of 
any other vapours or gases, is explained, by the molecular 
theory in the following way. 




MOLECULAR THEORY. 


107 


The theory supposes that liquid water consists of a num¬ 
ber of particles moving with different velocities in all direc¬ 
tions, but so acting on one another as to be continually 
interfering with each other’s motions. It also supposes that 
the vapour consists of a number of particles also moving with 
various velocities, but not interfering with one another until 
they come very close together, when repulsion takes place 
between them. The velocities both of the particles of gas,, 
or vapour, and of those of water, are increased with increase 
of temperature. The theory also supposes that there is a 
force acting for a very small distance on each side of the 
bounding surface of the liquid and gas, tending to prevent 
the escape of particles from the liquid. If a particle of liquid 
is moving towards the surface with sufficient velocity, it will 
have sufficient energy to carry it right through this field of 
force, and will then be free in space, and, in fact, will be a 
particle of gas. Now we have said that increase of tempe¬ 
rature increases the velocity of the particles of liquid, and it 
will therefore increase the number which will escape from 
any surface of the liquid in a second. This number will 
therefore depend upon the temperature of the liquid, and be 
also proportional to its surface. Now of the particles of gas 
outside, some will be moving towards the liquid and striking 
it will enter the liquid, where they will be, as it were, taken 
prisoners by the other particles, and ceasing to be particles 
of gas will become part of the liquid. Also, the number of 
those which enter the liquid per second will be proportional 
to the extent of the surface of the liquid and to the number 
of particles of gas in the unit of volume above it. It will also 
depend on the temperature of the gas. Now when the num¬ 
ber of particles of liquid which escape from each unit of area 
of its surface is equal to the number of particles of the gas 
which enter it through the same area , the number of particles 
of gas above the liquid will remain unchanged; in fact, the 
space will then be saturated with the vapour, and it may be 
shewn that this final state of things, or balance of exchanges, 
will not be affected by the presence of foreign particles with 
the vapour. This explains Dalton’s laws and also shews that 
the apparent rate of evaporation must depend upon the rate 
at which the vapour can get away from the liquid by dif¬ 
fusion through the air. 


108 


LATENT HEAT OF EVAPORATION. 


Latent Heat of Evaporation. 

170. When a liquid begins to boil, although heat is 
continually communicated to it and the temperature of the 
vapour is not above that of the liquid, yet as long as any of 
the liquid remains its temperature will continue unchanged, 
provided that its composition be not altered. (This provision 
excludes unsaturated solutions which become more concen¬ 
trated on boiling, and mixtures of liquids which undergo 
fractional distillation.) The heat which enters the liquid 
during the- process of boiling, as it does not raise the 
temperature, was supposed by Dr Black to become latent 
within the vapour, and this hypothesis seemed the more 
probable since this heat again becomes sensible when the 
vapour is condensed. We now know that the so-called latent 
heat really ceases to be heat, being entirely used up in doing 
work and causing the water to become vapour in opposition 
to molecular forces and to the pressure of the air. When the 
vapour is condensed a corresponding amount of work is done 
upon the particles, and the same amount of heat is again 
produced. 

Def. The • number of units of heat required to convert the 
unit of mass of a liquid or solid into vapour without change 
of temperature is called the latent heat of vaporisation , or, 
more frequently , the latent heat of the vapour. 

171. Soon after Dr Black enunciated his theory of latent 
heat, James Watt found that the latent heat of vaporisation 
of water diminishes as the temperature rises. The amount 
of heat required to raise the unit mass of water from 0° C. 
to any particular temperature and then to convert it into 
saturated steam, Regnault called the total heat of the steam 
at that temperature. The phrase is sometimes convenient 
though very unjustifiable. Begnault found that the total 
heat of steam at any temperature, t° C., may be represented by 

606*5 + -305 t. 

Assuming that the specific heat of water is always unity 
(which is not quite true), it follows that the latent heat of 
steam at t° C. must be equal to the total heat diminished by 


LATENT HEAT OF STEAM. 


109 


the t units required to raise the temperature of the water to 
t°. The latent heat of steam at t°C. will therefore be 
represented by 

606*5 — *695£. 

Putting t equal to 0 we have for the latent heat of 
aqueous vapour at the freezing point 606*5, while putting t 
equal to 100 we see that the latent heat of steam formed at 
the standard atmospheric pressure is 537. 

172. It is worthy of remark that (with the exception of 
certain mixtures of alcohol and water which have been shewn 
by Dr Duprb and Mr Page to have a greater specific heat 
than pure water) water has a higher specific heat than any 
other liquid or any solid; the latent heat of fusion of ice is 
greater than that of any other substance; and the latent heat 
of steam at the ordinary boiling point is greater than that of 
any other vapour. The latent heat of Alcohol is about 202*4, 
that of Ether about 90*5, and that of Bromine, about 45*6. 

173. The latent heat of evaporation of water, more 

generally called the latent heat of Fig. 30. 

steam , may be measured by means of 
the apparatus shewn in Fig. 30. A 
represents a flask containing boiling 
water, the steam from which escapes 
through the tube B ; C is a beaker 
containing a known weight, say 1000 j 
grains, of distilled water at a known 
temperature, say 14° C. 0 When the 
steam is escaping freely from B , its 
end is made to dip nearly to the bot¬ 
tom of the water in the beaker. After 
a short time the tube B is removed, 
and the temperature of the water in 
the beaker observed. Suppose it to be 20° C. The beaker 
is then weighed, and the difference between this and the last 
weighing gives the amount of steam which has entered it. 
Suppose^ this to be 10 grains'^ind suppose the temperature 
of the steam, as indicated by the thermometer in A , to be 
100° O. Then 10 grains of steam in being cooled from 100° C. 
to 20° C., have raised the temperature of 1000 grains of water 















110 


LATENT HEAT OF STEAM. 


6° C. Ten grains of steam therefore in condensing and cool¬ 
ing from 100° C. to 20° C., emit as much heat as would raise 
6000 grains of water 1° C. But 10 grains of water in cooling 
from 100° C. to 20° C., would emit sufficient heat to raise 800 
grains of water 1° C. Hence 10 grains of steam at 100° C., 
in condensing to water at 100° C., emit sufficient heat to 
raise 5200 grains of water 1° C. The latent heat of steam is 
therefore determined by this experiment to be 520. 

174. The result obtained in the last article is, obviously, 
too small, because we have neglected the heat taken up 
by the beaker as well as that lost to surrounding bodies. 
This source of error may be eliminated by emptying the 
beaker after the last weighing, placing in it 1000 grains of 
water at 14° C., as before, and slowly pouring into this a 
quantity of water at some known temperature, say 50° C., 
keeping the whole well stirred until the temperature of the 
water in the beaker is 20° C., the same as after the entrance 
of the steam. If about the same time be occupied in this 
process as in the admission of the steam, about the same 
amount of heat will be lost to surrounding bodies, and the 
same amount will be taken up by the beaker. Suppose the 
amount of water at 50° C., which has been poured in, to 
be 206 grains. Then since the 206 grains of water at 50° C., 
have produced the same effect as was produced previously 
b}^ the 10 grains of steam, it follows that 10 grains of steam 
at 100° C., in becoming water at 20° 0., give out as much 
heat as 206 grains of water in cooling through 30° C., or 
as much as would raise 6180 grains of water 1° C. Whence 
we get for the latent heat of steam the number 538. Its 
actual value at 100° C. is about 537. 

175. The calorimeter described in Art. 42 may with 
advantage be substituted for the beaker in this experiment. 
Care should be taken to protect the upper part of the flask 
and the tube from loss of heat by a jacket of cotton wool or 
some similar material, and a screen should be placed between 
the calorimeter and the source of heat to keep off radiation. 

176. The fact that heat is consumed by water in passing 
into the condition of vapour prevents the sudden generation 
of large quantities of steam under ordinary circumstances. 
If the latent heat of steam were zero, as soon as a quantity 


CONDENSATION. 


Ill 


of water reached the boiling point the whole would at once 
be converted into steam, and the heating of water in an or¬ 
dinary kettle to near the boiling point would be a highly 
dangerous operation. There are some bodies in which, when 
they pass into the gaseous condition, such passage is accom¬ 
panied by a chemical change which allows work to be done 
by the chemical forces, and heat to be generated instead of 
being absorbed. Gun-cotton, Dynamite, and the like, are ex¬ 
amples of such bodies, and they behave very like a substance 
whose latent heat of vaporisation is negative. 

177. If a vapour be cooled below the temperature at 
which its pressure is the greatest which can be exerted at that 
temperature by the vapour in contact with its liquid, conden¬ 
sation will generally commence, and if the temperature be 
lowered still further, or attempts be made to increase the 
pressure of the vapour by diminishing the space occupied by 
it, the condensation will continue, the space remaining always 
saturated. By the simultaneous action of cold and pressure 
Faraday succeeded in liquefying nearly all the gases known to 
him except oxygen, hydrogen, nitrogen, (air), marsh gas, and 
carbonic oxide. He expressed his opinion that at — 166° F. 
no amount of pressure would liquefy these gases, and until 
very recently they were called permanent gases. They obey 
“ the gaseous laws ” much more faithfully than do those gases 
which can be liquefied readily (Art. 119). Since Faraday’s 
time (in 1877) these gases have all been liquefied, and hy¬ 
drogen solidified by Cailletet and Pictet. Thilorier’s appa¬ 
ratus for the liquefaction of carbonic anhydride consists of 
two iron bottles connected by a tube. One of these vessels 
is placed in a freezing mixture of ice and salt, while carbonic 
anhydride is produced in the other by the action of sulphuric 
acid on chalk. The gas passes over and liquefies in the cold 
vessel. If the liquefied carbonic anhydride be allowed to es¬ 
cape into the air through a fine jet, the bottle being inverted 
for that purpose, the cold produced by the rapid evaporation 
causes some of the material to freeze, forming carbonic anhy¬ 
dride snow, which may be collected by discharging the liquid 
into a wooden box perforated so that the gas can escape, 
when the solid is left in the box. Andrews’ apparatus for the 
condensation of carbonic anhydride will be described in 
Art. 180. 


112 


ANDREWS’ APPARATUS. 


178. The temperatures and pressures at which several 
gases have been liquefied are given in the following table. 


Pressure i: 

Sulphurous Anhydride 
Chlorine 
Cyanogen 
Ammonia 

Sulphuretted Hydrogen 
Carbonic Anhydride 
Hydrochloric Acid 
Nitrous Oxide 


Atmospheres. Temperature. 

2 7° C. 


4 

15°5 

4 

15°-5 

6J 

10° 

17 

10° 

36 

0° 

40 

10° 

50 

7° 


179. The action of freezing mixtures de¬ 
pends upon the latent heat absorbed by bodies 
in fusing or evaporating. If ice and salt be 
pounded together, the ice melts through the 
action of the salt, absorbing the latent heat 
of fusion, and if the materials be originally 
at 0° C. a temperature of — 20° C. may be pro¬ 
duced. The action of sulphuric acid on crystals 
of sodic sulphate is very similar. The rapid 
evaporation of liquids produces still greater 
degrees of cold. If two watch-glasses be 
moistened with water and placed under the re¬ 
ceiver of an air-pump, by quickly exhausting 
the receiver the glasses may be frozen together. 
The evaporation of water in air at ordinary 
pressure will serve to freeze small quantities 
of water if the temperature of the air be 2° C., 
provided that it be perfectly free from vapour. 
By mixing solid carbonic anhydride with ether 
and allowing the mixture to evaporate in vacuo , 
Faraday obtained a temperature of — 110° C. 
By causing a mixture of carbonic bisulphide 
and liquid nitrous oxide to evaporate in vacuo, 
Natterer obtained a temperature which he 
estimated at — 140° C. 

180. Dr Andrews’ apparatus for the com¬ 
pression of gases consists essentially of a tube 
of glass, of which the upper portion has a very 
fine bore, while both the bore and external 
diameter of the lower part of the tube are 


Fig. 31. 

















CAILLETET’s APPARATUS. 


113 


-considerably greater. This tube contains the gas to be com¬ 
pressed. The lower part of the tube is immersed in mercury 
-contained in a test-tube which is suspended in a copper 
cylinder. The conical shoulder of the tube rests in a corre¬ 
sponding seat in the cover of the cylinder which is screwed 
down upon a flange attached to the top of the cylinder, a 
leather washer covered with lard being placed between the 
grooved surface of the flange and cover. The copper cylinder 
is filled with water, and a slender steel screw entering at 
the bottom serves to diminish the capacity of the cylinder, 
and thus to produce the requisite pressure. On screwing 
up the steel screw the pressure of the water drives the mer¬ 
cury from the test-tube up the thermometer-tube, compress¬ 
ing the gas above it. 

If the tube be filled with pure carbonic anhydride at 
13*1° 0. when the pressure reaches about 48 atmospheres the 
gas begins to liquefy, the pressure remaining constant until 
the whole has assumed the liquid condition. On increasing 
the pressure the liquid will be seen sensibly to contract. On 
diminishing the pressure the liquid again expands, and if the 
pressure be rapidly relieved the liquid will boil violently, 
bubbles of gas being formed in its midst as soon as the pres¬ 
sure becomes sensibly less than 48 atmospheres. At 2T5°C. 
carbonic anhydride requires a pressure of about 60 atmo¬ 
spheres to liquefy it, while at temperatures above 30‘9 0 C. no 
amount of pressure we can apply will reduce it to the liquid 
condition, but of this we shall speak shortly. 

181. The apparatus with which Cailletet first succeeded 
in liquefying air differed only from that of Andrews just 
described in the manner in which the pressure was produced, 
and in having a stop-cock by which the water could escape 
from the cylinder, thus allowing the pressure to be suddenly 
relieved. In Cailletet’s apparatus the cylinder was connected 
with a powerful force-pump, somewhat similar to the force- 
pump of a Bramah press, and the pressure applied by its 
means. The thermometer tube containing the gas was 
cooled by a freezing mixture to about — 29°C., and a pressure 
of about 300 atmospheres was applied, but under this pressure 
carbonic oxide, nitrogen, oxygen and hydrogen retained the 
gaseous state. On suddenly relieving the pressure by 
G. 8 


114 


PICTET’S APPARATUS. 


turning the stop-cock, the rapid expansion of the gas 
occasioned so great a diminution of temperature that in the 
case of each of these gases a liquid spray was produced in the 
tube. 

182. Pictet worked on a somewhat larger scale than 
Cailletet. By the employment of double-action pumps, 
which served to exhaust the gas from one vessel and to com¬ 
press it in another, Pictet liquefied a quantity of sulphurous 
anhydride in a large tube, aud by pumping the gas out from 
one end of the tube, liquefying it in a cold vessel by pressure 
and then causing the liquid to enter the other end of the 
tube, he kept up a constant circulation of the same sulphu¬ 
rous anhydride. In the interior of the sulphurous anhydride . 
tube was placed another tube into which carbonic anhydride 
passed from the vessel in which it was generated. The rapid 
and continued evaporation of the sulphurous anhydride 
under the diminished pressure kept up by the pumps cooled 
the carbonic anhydride so much as to liquefy it under the 
pressure to which it was exposed. The liquid carbonic 
anhydride then flowed into a tube, through the centre of 
which was passed a smaller tube into which was forced the 
air or other gas to be liquefied. A second set of pumps 
removed the carbonic anhydride as it evaporated, and forced 
the gas so removed back into the tube immersed in the 
sulphurous anhydride, thus keeping up a constant circulation 
of the carbonic anhydride. A third set of pumps forced air 
or any other gas to be examined into the narrow tube 
immersed in the liquid carbonic anhydride which was 
rapidly evaporating under the action of the pumps. The 
tube containing the air (or other gas) was provided with a 
stop-cock by which the pressure could be suddenly relieved. 
The temperature of the gas, already cooled by the evaporation 
of the carbonic anhydride, became so much lowered by the 
sudden expansion that a liquid spray was produced in all the 
cases tried, and it was stated that hydrogen became solidified 
into a grey metallic substance. 

183. M. Cagniard de la Tour in 1822 enclosed a quantity 
of alcohol in a tube so as to occupy about two-fifths of the 
volume of the tube. A small pellet of mercury separated 
the alcohol from the air, which at first filled the remainder 


THE CRITICAL POINT. 


115 


of the tube, and the compression of this air served to measure 
the pressure to which the alcohol was exposed. On raising 
the temperature to about 225°C. (according to Cagniard de 
la Tour) the alcohol suddenly disappeared, or rather, the 
surface separating it from its vapour vanished, the pressure 
recorded being about 129 atmospheres. In another experi¬ 
ment, when the alcohol filled much more than two-fifths of 
the interior of the tube, an explosion took place, but when 
the volume of the alcohol was much less, it all evaporated 
before reaching the temperature at which the surface van¬ 
ished in the first experiment. A similar result was obtained 
with ether, naphtha, and water, but in the case of water it 
was necessary to add a little sodic carbonate to prevent the 
solution of the glass. These experiments were afterwards 
repeated and the results verified by Faraday, and more 
recently by Andrews. As the temperature is raised the 
bounding surface of the liquid becomes less and less curved, 
indicating a diminution of the surface tension, and at the 
same time less distinct, until it becomes perfectly plane just 
before it vanishes altogether. Immediately after the vanish¬ 
ing of the surface a flickering haziness is sometimes noticed 
in the tube, as if some of the contents alternately became 
liquid and then gaseous again. It seems that as the tem¬ 
perature is raised the vapour becomes more and more dense 
through increased evaporation, while the liquid expands, 
becoming less dense, so that the properties of the two gra¬ 
dually approach one another, and at length the whole 
becomes apparently one continuous mass. This temperature, 
at which the liquid and the gaseous states merge into one 
another, has been called by Andrews the critical point. 

As the temperature is raised the latent heat of evapora¬ 
tion of liquids diminishes, indicating that less energy is 
required to effect the transformation of the liquid into the 
gas, and this diminution appears to continue without limit as 
the temperature approaches the critical point, so that when 
this temperature is reached the latent heat of evaporation 
becomes nil, the liquid and gaseous states being in fact iden¬ 
tical. When a substance is heated above the critical tem¬ 
perature it seems to be impossible to liquefy it by pressure. 
Faraday was of opinion that - 166°C. is above the critical 
temperature for air, oxygen, hydrogen, nitrogen, carbonic 


116 


THE CRITICAL POINT. 


oxide and marsh gas. Air can be easily compressed to a 
density far exceeding that of water without any apparent 
change taking place in its constitution. 

184. Dr Andrews has very carefully studied the be¬ 
haviour of carbonic anhydride when near the critical point by 
means of his apparatus for the compression of gases described 
in Art. 180. By surrounding the thermometer-tube by a 
rectangular case with plate-glass front and back, and filling 
this case with water whose temperature could be very accu¬ 
rately adjusted, he has found the critical temperature to be 
30*92° C. In order to obtain a substance in the critical state 
it is necessary not only to adjust the temperature to the 
critical point, but also the pressure to what may be called 
the critical pressure. These, two conditions will determine 
the volume of any given quantity of the substance, and 
therefore its density, so that we may speak of the critical 
temperature, critical pressure, and critical volume of a sub¬ 
stance. Hence the difficulty of observing the phenomena 
attending the passage of a substance through the critical 
point when sealed in a glass tube, for if the volume of the 
tube exceed the critical volume the substance will entirely 
evaporate before reaching the critical temperature, while if it 
fall short of the critical volume the liquid will expand till it 
fills the tube, and the substance will remain entirely in the 
liquid state until the tube bursts; or, if the tube be strong 
enough to resist the pressure, the liquid will pass by a con¬ 
tinuous process into the gaseous state, as the critical point is 
reached, without any change taking place in its appearance, 
and the contents of the tube will not be partly liquid and 
partly gaseous, so as to shew the bounding surface of the 
liquid when the critical point is reached. 

The critical temperature and pressure of some substances 
as determined by Dr Andrews are given in the following 
table: 


Carbonic Anhydride 

Temperature. 

30 0, 92 C. 

Pressure in 
atmospheres. 

75 

Ether 

187° ’5 

37*5 

Alcohol 

258° 7 

119 

Carbon Bisulphide 

262° -5 

66*5 

Water 

411° -7 

2 


leidenfrost’s phenomenon. 


117 


185. If the temperature of a substance be raised above 
the critical point, so that the whole becomes gaseous, and be 
then gradually lowered, the pressure being maintained above 
the critical pressure, the substance will pass continuously 
from the gaseous to the liquid state as the temperature 
passes through the critical point, no apparent change taking 
place in the nature of the contents of the tube; but on suffi¬ 
ciently diminishing the pressure after the temperature has 
fallen below the critical point the liquid will be seen to 
boil. 

186. By placing the tube of Andrews’ apparatus in a 
solar microscope in front of an oxyhydrogen or electric lamp, 
the radiation from the lamp suffices to raise the temperature 
of the tube above the critical .point for carbonic anhydride, 
and at the same time to project an image of the contents 
(magnified say 100 diameters) on a screen suitably placed. 
A blast of air from a bellows serves to lower the temperature 
below the critical point when required without interfering 
with the image on the screen. By this means all the phe¬ 
nomena above described as attending the passage of carbonic 
anhydride through the critical point can be exhibited. 

187. If a clean metal plate be heated to redness and a 
drop of water placed upon it by means of a pipe, the drop 
will evaporate but slowly, provided the temperature of the 
metal be kept up, but if the metal be allowed to cool, the 
drop will presently pass into vapour with explosive violence. 
If the surface of the metal be slightly convex upwards, the 
drop can be easily held at the highest point of the surface by 
means of a cold wire inserted in the drop, but not touching 
the hot metal. It is then easy to see that the drop is not in 
contact with the metal surface, but is supported slightly 
above it, as shewn in Fig. 32. That Fig. 32. 

the drop is not in contact with the hot _ 

metal may also be shewn by connecting the ' 
wire which is inserted into the drop with one pole of a 
battery, the other pole being connected through a galvano¬ 
meter with the hot plate. In this case no deflection of the 
galvanometer will take place so long as the plate is suffi¬ 
ciently hot to support the drop as above described, but if the 
temperature be lowered till vapour is produced with ex- 




118 


THE SPHEROIDAL STATE. 


plosive violence the galvanometer will at the same time be 
deflected, indicating that the drop has come into contact 
with the plate, which of course accounts for the sudden 
generation of steam. So long as the drop is supported with¬ 
out coming into contact with the hot metal, its form is 
approximately spheroidal, though flatter at the lower than 
at the upper surface, and this condition of the drop is called 
the spheroidal state. Having been first carefully examined 
by Leidenfrost, it is frequently known as Leidenfrost’s phe¬ 
nomenon. 

188. All liquids which readily evaporate can be made 
to assume the spheroidal condition; but for a given metallic 
surface, the lowest temperature at which the spheroidal con¬ 
dition can be produced depends on the nature of the liquid 
and the pressure to which it is exposed. As a general rule 
the more volatile the liquid the lower the temperature re¬ 
quired, while for a given liquid reduction of pressure allows 
diminution of temperature, since it facilitates evaporation. 

The proximity of the heated metallic surface causes rapid 
evaporation to take place from the lower surface of the drop, 
and this rapid production of vapour from one surface only 
prevents the drop approaching the metal plate within a 
certain distance (for as it comes nearer the rate of evapora¬ 
tion must increase), in the same way as the expulsion of a 
stream of water from the stem of a ship propels the ship, or 
the expulsion of the shot from a gun causes the latter to 
kick; or again, the expulsion of the steam-jet from Hero’s 
engine or “ the little marvel ” produces rotation of the boiler. 
Any circumstance which accelerates evaporation of course 
facilitates the assumption of the spheroidal condition, but if 
the liquid once comes absolutely into contact with the metal, 
it becomes rapidly heated throughout and boils with ex¬ 
plosion. 

189. It was by availing himself of the spheroidal state 
of volatile liquids that Faraday was able to freeze water and 
mercury in a white-hot platinum crucible. By rapidly 
injecting a mixture of liquefied sulphurous anhydride and 
ether into the hot crucible the liquid was made to assume 
the spheroidal condition, so as to form a large “ drop ” with- 


THE SPHEROIDAL STATE. 


119 


out coming into contact with the vessel. Rapid evaporation 
quickly lowered the temperature of the drop sufficiently to 
freeze a small quantity of mercury held in a spoon near its 
centre. By employing a solution of solid carbonic anhydride 
in ether, in place of the mixture first used by Faraday, the 
experiment is greatly facilitated. 

190. If a tolerably large spheroid of water be formed in 
a clean platinum cup it will be frequently seen to assume a 
beaded appearance, always exhibiting however an even num¬ 
ber of beads around its circumference, as shewn by the con¬ 
tinuous lines in A 3 , B 3 , C 3 (Fig. 33). On examining the drops 

Fig. 33. 



carefully the outline of the beads wiH be seen to be con¬ 
tinued in a fluted form within the drop as shewn by the 
dotted lines in A s , B 3 , C 3 . If the room be darkened and the 
drop illuminated by electric sparks it will be seen to be 
constantly changing its form. Thus, if when examined by a 
continuous light it present eight beads as in B 3 , when illu¬ 
minated by the sparks it will present four beads and four 
flutes, sometimes appearing as B x and sometimes as R 2 . The 
drop is in this case vibrating like a bell which is sounding 






120 


SUBLIMATION. 


the second harmonic above the fundamental note, and there¬ 
fore possessing eight vibrating segments, and the figure B a 
seen by a continuous light is but the superposition of the 
images of the drop in its extreme vibration forms shewn at 
B x and Z? 2 . It is easy to obtain all the forms shewn in fig. 
31, the decagon, C 3 , being apparently an especial favourite,, 
but generally the number of segments diminishes as evapo¬ 
ration reduces the size of the drop. Sometimes the drop 
will rotate about a vertical axis while vibrating, and this of 
course multiplies the apparent number of vibrating segments 
when viewed by a continuous light, but the sparks soon 
indicate the true state of the case. 

191. Many accidental causes may serve to start vibra¬ 
tions in a spheroid. Sometimes a quick but gentle touch 
with a hot wire will start them, but if the spheroid be left 
to itself something generally happens to produce a vibration,. 
Once set up, the production of vapour is a sufficient cause to 
sustain them, for more vapour will be produced from the 
projecting segments than from the others, and this vapour 
will escape from underneath them and so press against their 
edges as they recede, while the escape of vapour past the 
edges of the advancing segments will be somewhat less. We 
thus have a periodical force and supply of energy acting in 
such a manner as to sustain the vibrations. 

192. Many solids evaporate at temperatures below that 
at which they melt under ordinary pressure, and increase of 
pressure or diminution of temperature causes the vapour at 
once to return to the solid form. The direct passage of a 
vapour into a solid is called sublimation. Camphor, iodine, 
ammoniacal salts, and some other volatile solids frequently 
sublime upon the surfaces of vessels containing them. When 
aqueous vapour is condensed upon surfaces at a temperature 
below the freezing-point hoar-frost is produced, which is 
consequently sublimed water. 

If a block of ice be placed in a vacuum at a temperature 
below the freezing point it will evaporate until the pressure 
of the vapour attains a certain amount depending on the 
temperature. Eegnault has investigated the pressure of 
aqueous vapour in the presence of ice through a range of 
several degrees below 0° C. By carefully cooling water below 


THE TRIPLE POINT. 


121 


0° C., so as not to cause it to solidify, he also determined the 
pressure of aqueous vapour in the presence of water for a 
few degrees below 0° C., and found the result was not quite 
the same as when only ice was present. There is, however, 
a particular temperature at which water, ice, and aqueous 
vapour can exist within a closed vessel, no other substance 
being present in the enclosure. The necessary condition for 
such coexistence is obviously that the pressure of aqueous 
vapour at this temperature should be the same whether it be 
in the presence of ice or water, and should be the pressure 
for which the existing temperature is the melting point of 
ice. This temperature is called the triple point; it is about 
0-007° C. 

Some other properties of steam will be mentioned in 
Chapter XII. 

193. It may be of use briefly to trace the changes which 
take place in a mass of ice when heated. 

Suppose we have a pound of ice at — 20° C. When 
heated it expands, its coefficient of expansion being about 
*00012 per 1° C., and its specific heat about *5. It will thus 
absorb about 10 units of heat, while its temperature is raised 
to 0° C., before it begins to melt. The substance will then 
remain at this temperature till it has absorbed about 79*5 
units of heat, when it will all have been converted into water, 
and in the transition its volume will have contracted by 
about 9 per cent. The temperature will then go on increas¬ 
ing steadily, the water contracting in bulk till its temperature 
reaches 4°C., after which it will continue to expand until 
about 101 units of heat have entered the water, when its 
temperature will be 100° C., and its volume will have increased 
by rather more than 4 per cent, of its volume as water at 
0° C. The water will then begin to boil, and if the heat be 
continued, the whole will pass off as steam, absorbing in the 
process about 537 units of heat, and expanding to about 1600 
times the volume of the water, the barometer being supposed 
to stand at 30 inches. Thus the amount of heat absorbed in 
the transformation of a pound of ice at — 20° C. to steam at 
100° C. is 

10 4- 79*5 4-101 4 537 units = 727*5 units, 
or, as much as would raise 727’5 lbs. of water through 1° C. 


122 


THEORIES OF EVAPORATION. 


The earliest theories with which we are acquainted 
assumed that vapour consisted of a compound of water with 
fire, which rendered the vapour light and caused it to ascend. 
When particles of vapour were blown together, the fire 
particles were shaken off and the water fell as rain. 

The supporters of another theory held that vapour 
consisted of vesicles, or little balloons of water filled with an 
aura, which was specifically lighter than air and caused 
the vesicles to ascend. 

Others again held that the air was the cause of evapo¬ 
ration, and that the air held aqueous vapour in chemical 
solution. This theory was disproved by De Saussure, who 
shewed that aqueous vapour was produced in the vacuum of 
.an air-pump to the same extent as in the air. 


CHAPTER VII. 


EFFECTS OF HEAT UPON THE ’MECHANICAL, MAGNETIC, AND 
ELECTRICAL PROPERTIES OF BODIES. THERMO-ELEC¬ 
TRICITY. PELTIER EFFECT. THERMO-PILE. 

194. We have seen (Art. 64) that a piece of India- 
rubber stretched by a weight will contract if heated. Hence 
it appears that in the case of India-rubber the elasticity is 
increased by raising the temperature. The reverse is the 
case with the majority of bodies which become less and less 
elastic as their temperature is raised, till at length they 
become viscous fluids. The ultimate strength of materials is 
also affected by change of temperature. Wrought iron is 
said to have the greatest strength to resist tension near the 
boiling point of water. When the temperature is raised 
much above this the strength of the iron rapidly diminishes. 
It is for this reason that both wrought and cast iron are 
almost useless as weight bearers in the construction of fire¬ 
proof buildings. 

195. By raising solid bodies to a high temperature and 
then slowly or rapidly cooling them their physical constitu¬ 
tion may sometimes be changed considerably. By very 
slow cooling from a high temperature some bodies are ren¬ 
dered soft and tough, while they become hard and brittle if 
cooled rapidly. Thus steel may be made very soft and 
pliable by heating it to redness and cooling it very slowly, 
but if cooled from a red heat by plunging it into water it 
becomes sufficiently hard to scratch glass. Steel is generally 
tempered by first hardening it and then heating it to a 
certain temperature, depending on the degree of hardness 
required, and allowing it to cool rapidly from this tempera¬ 
ture. The higher the temperature to which the steel is 


124 


TEMPERING AND ANNEALING. 


raised in the second heating (such temperature being kept 
considerably below that to which it was previously raised to 
harden it) the softer is the steel. If a piece of steel exposing 
a bright and clean surface be heated in air a layer of oxide 
is formed upon it which exhibits the colours of thin films. 
The thickness of this layer, and therefore the colour pre¬ 
sented, depends on the temperature. In tempering steel 
after hardening it by heating it to bright redness and cooling 
it suddenly in water, a small portion of the surface is made 
bright and the temperature acquired in the second heating 
is determined by the tint exhibited. At about 220° C. a 
faint straw-colour begins to appear. This deepens into 
yellow at about 245° C. and brown at 260° C. As the tem¬ 
perature is increased the brown gradually shades off into 
purple; and the surface becomes blue at about 320° C. The 
edges of tools for cutting metal are tempered at a straw- 
colour; cutting-tools for wood, knives, &c., at a brown; 
springs, saws, and instruments requiring great flexibility, at 
a purple or blue. In tempering chisels, turning-tools, &c., 
it is convenient to heat the end remote from the edge, 
allowing the heat to be conducted towards the edge and 
plunging it in water as soon as the edge reaches the proper 
tint. By this means the edge becomes the hardest portion 
of the instrument. 

If glass be rapidly cooled from a high temperature it 
becomes very brittle, and the slightest scratch upon its 
surface will frequently occasion its fracture. This liability 
to fracture is in great part due to a state of strain de¬ 
veloped in the glass through the rapid cooling. Kupert’s 
drops consist of pear-shaped drops of glass which are allowed 
to fall in a melted state into cold water. The exterior 
portion thus becomes solidified, while the interior is still 
at a red heat. As the interior cools the glass tends 
to contract, but is kept stretched by the outer envelope, 
which has become rigid. If the interior be disturbed by 
breaking off the tail of the drop, this state of strain is re¬ 
lieved and the glass crumbles to powder with explosive 
violence. The state of strain into which glass is thrown by 
rapid cooling is made manifest by examining it with polar¬ 
ised light, when the unannealed glass produces colours like 


ELECTRICAL RESISTANCE. 


125 


thin plates of mica or other doubly refracting crystals. Glass 
is annealed by cooling it very slowly in an annealing oven. 

Bologna flasks are small flasks or bottles which are 
allowed to cool rapidly after having been blown. By this 
means the exterior portions become solid before the interior 
have cooled to the same temperature, and as the interior 
portions subsequently harden and contract they are thrown 
into a state of tension by their cohesion to the external 
layers. Such flasks will stand a great deal of violence so 
long as the interior surface is not scratched, but the slightest 
scratch by a grain of sand on the internal surface causes the 
flask to fly to pieces. Injury to the outside of the flask is 
like a saw cut made in the upper surface of a beam supported 
at the ends and loaded in the middle. Injury to the interior 
is like a cut made in the lower surface of the same beam and, 
like a little rift on the edge of a piece of paper under tension, 
not only diminishes the available section of the material but 
concentrates the tension around the end of the rift and leads 
to inevitable destruction. The exterior layers of the flask 
are subject to pressure, like the upper layers of the beam; 
the interior layers to tension. 

196. Copper when heated behaves differently from steel, 
since it is rendered soft and malleable by heating it to red¬ 
ness and cooling it suddenly in water. Continual hammering 
renders copper and brass hard and brittle, and in shaping 
these metals under the hammer it is necessary frequently to 
anneal them by heating them and then cooling them quickly. 
If the copper be required hard in order to resist rubbing, it 
is best to subject it to the hammer after it has been heated 
for the last time. 

197. The relations of many bodies to magnetism and 
electricity undergo considerable variation as their temperature 
is changed. Thus steel magnets become weaker as their tem¬ 
perature is raised, but if the range through which they are 
heated be only a few degrees from ordinary temperatures, 
they very nearly recover their original strength on cooling. 
If, however, a steel magnet be heated to redness, it com¬ 
pletely loses its magnetism and does not recover it as it cools. 

Different bodies offer different resistances to the passage 


126 


ELECTRICAL RESISTANCE. 


of an electric current through them. The resistance of any 
conductor is generally expressed in terms of that of a certain 
standard wire at a defined temperature. It has been found 
that the resistance of all bodies which conduct electricity 
like metals without themselves undergoing any change is 
increased by increase of temperature, but that the resistance 
of bodies in which the passage of electricity is accompanied 
by chemical decomposition, that is, of electrolytes , is dimin¬ 
ished by increase of temperature. Glass belongs to the 
latter class, and if two pieces of metal be connected with the 
electrodes of a Holtz’s machine, and united by a few inches 
of glass rod, when the glass is red hot the electricity passes 
quietly through it. As the glass cools the passage of the 
electricity is accompanied by a beautiful glow, very apparent 
in a darkened room, the colour of the light depending on 
the character of the glass, but long before the glass has. 
cooled to the ordinary temperature the electricity ceases to 
pass through it to any sensible extent, and prefers to make 
its way as a “ spark ” through the air. 

198. As a general rule the electric resistance of pure 
metals changes more for a given change of temperature than 
that of alloys. It has been found that the resistance of 
metals increases pretty uniformly with the temperature, and 
this property has been utilized for the purpose of determining 
the temperature of furnaces. The electric pyrometer consists 
of a fine coil of platinum wire connected to terminals whose 
resistance is very small compared with its own. This coil is 
placed in the interior of the furnace and a current being sent 
through it its resistance is measured in the usual manner, 
and its resistance and rate of increase per degree at ordinary 
temperatures being known, the temperature to which it is 
exposed can be determined. 

199. If an electric current be sent through a conductor 
heat is produced, the amount generated per second being 
proportional to the resistance of the conductor and to the 
square of the current conjointly. Hence a strong current 
will quickly raise to a white heat a fine platinum wire whose 
capacity for heat is small. A wire which can be so heated 
is very convenient for many purposes, since it may be placed 
when cold in positions in which it is impossible to place a 


PELTIER EFFECT. 


127 


heated body, and may be subsequently heated when re¬ 
quired. A platinum wire heated to redness by a current 
from a battery is sometimes employed by surgeons for cutting 
and cauterising. 

Incandescent electric lamps consist of specially prepared 
carbon filaments made from cotton, bamboo fibre, or other 
material, which are placed in small glass globes exhausted of 
air as far as possible by mercury pumps. The ends of the 
carbons are cemented, electrotyped or otherwise connected to 
platinum wires fixed into the glass and terminating on the 
outside in loops which form the electrodes of the lamp 
When an electric current of sufficient strength is sent 
through the filament it is raised to a bright white heat. 

200. When an electric current passes from one metal to 
a different metal heat is produced or absorbed at the junction 
according to the direction of the current and independently 
of the resistance of the metals. The rate at which heat is 
produced or absorbed in this action is simply proportional to 
the current and not to its square. This phenomenon was 
first noticed by Peltier, and is known as the Peltier effect. 
It may be readily rendered manifest by soldering a small bar 
of bismuth and one of antimony together, and placing the 
junction within the bulb of an air thermometer. If the 
current from a single Grove’s cell be passed through the bar 
heat will be produced when the current passes from antimony 
to bismuth, and cold when it passes in the opposite direction. 
Too strong a battery should not be used or the heat due 
to the simple resistance of the metals will conceal the Peltier 
effect. 

201. If two different metals be soldered or twisted 
together at each end, so as to form a continuous circuit, no 
current of electricity will pass round it, provided that both the 
junctions are at the same temperature, but if one junction 
be at a higher temperature than the other, a current will 
generally be produced. In the last article we stated that a 
current of electricity passing from one metal to another 
generally heats or cools the junction. In the case here con¬ 
templated the current passes in such direction as to cool the 
hot and heat the cold junction, thus tending to equalise the 


128 


THERMO-ELECTRICITY. 


temperature of the circuit. It is clear that it cannot pass in 
the other direction, as in this case a current once started in 
a circuit of two metals originally of uniform temperature 
would increase indefinitely, heating one junction and cooling 
the other at a continually increasing rate. 

202. In the following list the metals are so arranged 
that if any two of them be connected to form a circuit 
at ordinary temperature, one junction being slightly hotter 
than the other, the current will flow across the hot junc¬ 
tion from the metal which stands higher in the table to 
the other. Thus, if the metals be antimony and bismuth the 
current will flow from bismuth to antimony across the hot 
junction. If they be copper and iron it will flow from copper 
to iron across the heated junction, and if they be bismuth 
and iron it will flow from the bismuth to the iron across the 
heated junction. 


Thermo-electric Arrangement of Metals. 


1 Bismuth. 

2 Mercury. 

3 Lead. 

4 Tin. 


7 Gold. 

8 Silver. 

9 Zinc. 
10 Iron. 


5 Copper. 

6 Platinum. 


11 Antimony. 


The position of a metal upon the list frequently depends 
upon its purity and mechanical condition. 

203. If a circuit be formed of copper and iron and a 
galvanometer introduced by cutting the copper wire and 
connecting the ends with the electrodes of the galvanometer, 
and if one of the junctions be heated it will be seen that the 
current increases until a temperature of about 260° C. is 
reached; when, on heating the junction still more, the current 
diminishes, and when the hot junction is as much above 
260° C. as the cold junction is below this temperature, the 
current ceases. On raising the temperature still higher the 
current is reversed in direction, and we have thermo-electric 
inversion , the current passing from iron to copper across the 
hot junction. The temperature at the hot junction when 


THERMO-ELECTRICITY. 


129 


the current begins to diminish is called the neutral tempera¬ 
ture of iron and copper. Professor Tait has shewn that the 
electro-motive force in a thermo-electric combination of two 
metals is proportional to the product of the difference of 
temperature of the junctions and the difference between the 
mean of the temperatures of the junctions and the neutral 
temperature of the two metals. Thus, in the case of copper 
and iron, if the hot junction be at 220 ° C. and the cold at 
20 ° C., the electro-motive force is proportional to 

(220 - 20 ) ^260 - 220 + 20 j ) or 2 00 x 140, while if the hot 

junction be at 600° and the cold at 40° C., the force is pro¬ 
portional to 

(600 — 40) ^260 — 600^+ ^ or 5 qq x ( — 60), the negative 

sign in this case indicating that the direction of the current 
has been reversed. 

If one junction of a copper-iron couple be at the neutral 
temperature and the other junction below the neutral 
temperature a current will flow in the circuit, the cold 
junction will be heated, but the hot junction will not be 
cooled, as at the neutral temperature the two metals behave 
like one. The heat must therefore be absorbed from the iron 
or copper or both. This was predicted by Sir William 
Thomson, who found experimentally that when heat flows 
from cold to hot in copper or from hot to cold in iron it cools 
the metal, and heats it when it flows in the opposite direction. 
This is known as the Thomson effect. 

204. Thermo-electric combinations are sometimes em¬ 
ployed for determining the temperature in situations where 
ordinary thermometers cannot be used. Thus, the tem¬ 
perature at the bottom of the sea may be determined by 
employing long wires of copper and iron in circuit with a 
galvanometer. One of the junctions is caused to descend to 
the sea bottom and the other placed in a bath whose tem¬ 
perature is adjusted until there is no current through the 
galvanometer. The temperature of the bath must then b& 
the same as that of the sea bottom, and can be read by an 
ordinary thermometer. 

G. 


9 



130 


THERMO-PILES. 



205. If several bars of bismuth and anti- Fig - 34 - 
mony are united, as in the figure, and the 
alternate junctions heated, the electro-motive 
force in the circuit is the sum of the forces due 
to each pair of consecutive junctions, and by 
using a large number of bars a very sensitive 
instrument may be constructed. The thermo¬ 
electric pile consists of a number of such bars 
sometimes united in the form of a cube, the alter¬ 
nate junctions being on opposite faces. If the Fig. 85. 
extreme bars are connected by a 
•yvire passing round a freely sus¬ 
pended magnetic needle, any dif¬ 
ference in the temperatures of the 
opposite faces of the cube at which 
the junctions are situate, produces 
a corresponding deflection of the 
needle, the pile thus acting as a 
very delicate differential thermo¬ 
meter. One of the faces of such a 
pile is shewn in fig. 35. 



Various forms of thermo-electric piles have been con¬ 
structed in order to obtain strong electric currents for electro¬ 
typing, electro-plating, driving electro-magnetic engines, and 
other similar purposes, but in all the very powerful thermo¬ 
electric combinations which have hitherto been tried one at 
least of the metals or alloys employed is very brittle, and 
liable to crack through rapid changes of temperature or 
through slight mechanical violence, and unless used with 
very great care they are soon rendered inefficient. 

















CHAPTER VIII. 


ON THE TRANSMISSION OF HEAT. 

206. There are three methods generally enumerated 
by which heat may be transmitted from one point to another. 
They are, 

I. Conduction. 

II. Convection. 

III. Radiation. 

Heat is said to be transmitted by conduction when it passes 
from hotter to colder portions of the same body, or from a hot 
body to a colder body in contact with it: the heat in this 
case being transmitted from each particle of the material 
of the body to contiguous particles in directions in which the 
temperature decreases. A familiar example of conduction 
is found in the transmission of heat along a poker, one end 
of which is placed in the fire. 

Heat is transmitted by convection when the material body 
containing the heat is carried from one point to another. 

Thus if hot water is carried in a bucket or conveyed in 
pipes from one point to another, the heat contained in the 
water, as well as the water itself, is said to be transmitted 
by convection. 

Heat is said to be transmitted by radiation when it passes 
from one point to another irrespective of the temperature of 
the medium through which it passes. 

Thus we feel the sun’s rays to be warm, and a thermo¬ 
meter exposed to them will indicate a temperature con¬ 
siderably above 0°C., though the air through which the 
rays pass may be at a temperature below the freezing point. 

9—2 


132 


RADIATION. 


Bodies which, like air, allow of the passage of radiation 
through them without themselves becoming heated, are called 
Diathermanous, while bodies which, like the metals, do not 
possess this property are called Adiathermanous. 

207. This last mode of transmission of heat differs from 
the two preceding, inasmuch as the heat does not pass 
from one point to another as heat, but is converted into 
another form of energy which is only reconverted into heat 
under special circumstances; and in some cases is capable 
of causing the sensation of light if allowed to enter the eye, 
or even of producing a photographic picture on a properly 
prepared surface, by inducing chemical or molecular changes 
in the constitution of the^body on which it falls. The trans¬ 
mission of heat by radiation is therefore a case of double 
transformation of energy , and may be classed with several 
other ways in which heat appears to be communicated from 
one place to another, though, during its passage, it is really 
not heat at all; as, for example, when some of the heat 
generated in the furnace under the boiler of a steam-engine 
is converted into the energy of motion of the parts of the 
machinery, and partially reconverted into heat by the friction 
of the bearings, &c.; or, when the heat applied to one set 
of junctions in the thermo-electric pile is converted into the 
energy of an electric current, and reconverted into heat at 
the opposite set of junctions, and in the wire through which 
it passes. The phrase “radiant heat” is therefore unscientific, 
and it is best to employ the term radiant energy instead. 


Conduction of Heat. 

In the distinctions made in the last article attention is 
drawn to the fact that when heat passes by conduction it 
always flows from hotter to colder portions of matter, existing 
always as heat in the particles of the body through which it 
travels. Radiant energy moves with the velocity of light 
and subject to the same laws as light (see Art. 232), while 
the same beam may pass through various bodies differing in 
temperature to any extent and arranged in any order. It is 
not in fact taken up by the material particles of the bodies 


THERMAL CONDUCTIVITY. 


138 


through which it passes, but is supposed to consist of transverse 
vibrations of the luminiferous ether. If the material particles 
of the body do take up the energy of the vibrations and be¬ 
come heated thereby we have a case of absorption, and the 
energy so taken up ceases to be transmitted by radiation. 

208. If we enter a very cold room, and touch various 
articles in the room, we find that the metal articles feel 
coldest of all, and of these we may notice that large masses 
of silver or copper feel especially cold to the touch, while 
the wooden furniture produces the sensation of cold in a 
less degree, and the hearth-rug, or other woollen materials, 
hardly seem cold. Now if a thermometer be brought into 
contact with all these articles in succession it will register 
the same temperature, the reason of the difference to the 
touch being that the metallic bodies transmit heat through 
their own masses, and so take it away from the hand, much 
more readily than wood, and wooden articles much more 
readily than woollen materials. In fact, the bodies which 
feel colder than others, seem so, not because they are at 
lower temperatures, but, because they are better conductors 
of heat. In high latitudes, where the cold is very intense, 
contact with a piece of metal exposed to the weather will 
inflict a blister on the hand. 

For a reason similar to the above, in the hot room of a 
Turkish bath, metallic objects feel much hotter than others, 
and will inflict a bum, so that spectacles with metal frames 
have to be dispensed with. The human body is prevented 
from being unduly heated when exposed to a high tempera¬ 
ture by the evaporation going on from its surface. 

209. From what we have just said we see that different 
bodies possess different powers of conducting heat, or different 
thermal conductivities. 

The fact that there is a difference in the thermal con¬ 
ductivity of different substances, may be readily shewn by 
taking three tea-spoons, made of silver, lead and bone re¬ 
spectively, and placing their bowls in hot tea. The handle 
of the silver spoon soon becomes too hot to touch without 
inconvenience, and in the same time that of the leaden spoon 
becomes hot, but less so than the former, while the handle 


134 COMPARISON OF THERMAL CONDUCTIVITIES. 

of the bone spoon is only slightly heated. Silver spoons 
may be distinguished from those made of other metals and 
plated by the readiness with which they transmit the heat 
of the tea to the hand. It is on account of the low conduc¬ 
tivity of such substances as wood, bone, glass, &c., that they 
are employed as handles for vessels containing hot bodies, 
or inserted between the handles and the vessels themselves. 
The value of blankets depends upon the extremely low con¬ 
ducting power of woollen materials, and a blanket will serve 
equally to keep a warm body from cooling, or to keep ice 
from melting. The low conductivity of felt is utilised in the 
Norwegian cooking pot, which is a box lined with many 
layers of felt. The saucepan containing the food is first 
heated, and then placed in the box and shut in, when it will 
retain for a long while a temperature sufficiently high to 
carry on the operation of cooking. 

210 . The measure of the thermal conductivity of a 
substance will be defined in Art. 214. The relative con¬ 
ductivities of different substances may be compared by means 
of the arrangement shewn in fig. 36, and known as Ingen- 
houz’s apparatus. 

This consists of a 
trough A B con¬ 
taining oil, which 
can be heated to 
a high tempera¬ 
ture. Equal bars 
of the solids whose thermal conductivities are to be compared 
are taken, and one end of each is passed through one side of 
the vessel AB into the oil. The surface of each bar is coated 
with a thin layer of wax, so that each exposes the same 
surface to the air, and will therefore cool at the same rate, 
other things being the same. Now if the oil be heated to, 
say, 200° C., and sustained at that temperature, the bars will 
gradually become hot, and the heat will travel towards their 
extremities which are distant from AB, the wax melting at 
increasing distances along each bar. After a time, which will 
be different for the different bars, it will be found that the 
boundaries between the melted and solid wax no longer travel 
towards the ends of the bars, but remain stationary, however 


Fig. 36. 





CONDUCTION OF HEAT. 


135 



long the temperature of the oil may be maintained. The 
temperature of every point Fm 37 

of the bar then remains un- K 
altered, and if DE, fig. 37, re¬ 
present the bar and S any 
point upon it, this will be the 300c 
case when the rate of decrease 
of the temperature at S as we 
go towards E is such that the 
flow of heat across the section of the bar at S is equal to 
the rate at which heat is dissipated by the portion of the 
bar beyond S. The temperature of the bar will decrease 
in going from D to E at a rate diminishing as the distance 
from D increases. If at every point of the bar a line be 
drawn at right angles to its length, and proportional to 
the excess of the temperature of the bar at that point, 
above that of the air, the extremities of these lines will 
lie on a curve similar to KL. Now the wax on the bars 
will be melted to distances where the temperature of the 
bars is the melting point of wax, and it may be shewn 
that when the wax ceases to melt any farther, if all the 
bars are of the same section, the squares of these distances 
are proportional to the thermal conductivities of the bars. 
Hence we have only to measure from the vessel of oil the 
distance on each bar along which the wax is melted in order 
to compare the thermal conductivities of the materials of 
which the bars are composed. The bars are generally in¬ 
serted into small tubes which pass through the oil across the 
box, and are soldered to each side of the box so that the 
tubes are surrounded by oil just as the tubes in a locomotive 
boiler are surrounded by water. 


211. It should be borne in mind that the thermal con¬ 
ductivities of different bars cannot be determined by heating 
one end of each to the same temperature, and observing the 
time required for points on all the bars at the same dis¬ 
tance from the heated ends to be raised to a given tem¬ 
perature. For instance, in the experiment just described, we 
might observe the time required for the wax to be melted 
on each bar at a distance of three inches from the trough, 
after pouring the hot oil into the latter. We could not. 





136 


CONDUCTION OF HEAT. 


however, in this way compare the thermal conductivities of 
the bars because their capacities for heat per unit of volume 
may be different; thus, of two bars A and B, A may have 
the greater conductivity, but if its capacity for heat per 
unit of volume be also greater than that of B, the time re¬ 
quired to melt the wax on A may be greater than that 
required to melt it on B to the same distance. In order to 
compare the thermal conductivities, we have therefore to wait 
until the temperature of any point of the bars has ceased 
to change, or till the flow of heat has become “ steady,” 
as explained in Article 213. 

212 . The statement made in the last Article can be 
well illustrated by simultaneously placing a bar of iron and 
a bar of bismuth, of the same dimensions and each about 
1 in. in length, upon end on a hot copper plate, a small 
piece of wax or paraffin having been previously placed on 
the upper end of each bar. (Care should be taken that the 
temperature of the copper is insufficient to melt the bismuth.) 
If the bars be not too long and the temperature of the hot 
plate be sufficiently high the wax or paraffin upon the bis¬ 
muth bar will begin to melt before that upon the iron bar, 
but the rate at which the melting will progress after it has 
commenced will be much greater on the iron than on the 
bismuth, so that if the quantity of wax or paraffin is large 
that on the iron will be completely melted before the other. 
Now the thermal conductivity of iron is more than six times 
that of bismuth, yet the upper end of the bismuth becomes 
first heated to the melting point of wax or paraffin because 
the specific heat of iron is nearly four times that of bismuth : 
but after that the iron has become sufficiently heated to 
commence the fusion, heat is conducted along it much more 
rapidly than along the bismuth. 

If the bars be of considerable length and be coated all 
over with paraffin, it will be seen that the paraffin will melt 
at first more quickly on the bismuth bar, but after it has 
melted up the bismuth bar for perhaps an inch that on the 
iron bar will overtake it, and finally the wax on the iron 
bar will be melted over more than twice the distance of that 
on the bismuth bar. 


MEASURE OF THERMAL CONDUCTIVITY. 


137 


213. If one side of a plate of metal be kept in contact 
with water whose temperature is sustained at 100° C., while 
the other side is kept in contact with melting ice, heat will 
flow through the metal by conduction from the hot to the 
cold side, and after a short time the metal will acquire its 
permanent condition with regard to temperature under 
these circumstances. When this is the case, the flow of 
heat through the metal will be the same at all parts, and 
continue constant so long as the temperature of the faces is 
kept unaltered. The flow is then said to be steady. The 
flow of heat across the unit of area of any plate of given 
material is found to vary inversely as the thickness of the 
plate, and directly as the difference between the temperatures 
of the two faces. Now suppose the thick 
plate AB, fig. 38, to be made up of a 
number of thin plates of equal thickness, 
as in the figure. Then when the flow of 
heat is steady, the amount of heat which 
crosses each of the thin plates in a second 13 
is the same, and therefore the difference fl ' c 
between the temperatures of the opposite 
faces must be the same for each plate, and 
the temperature of the thick plate must 
decrease uniformly from 100° C. on the one side to 0° C. on 
the other side. 

If we take two plates of the same material and thickness, 
and suppose no heat to escape at the edges, if one side of 
each be kept at 100° C. and the other at 0° C., the amount of 
heat which will flow through each of the two plates in a 
given time will be obviously proportional to their areas. 

214. Def. The number of units of heat which flow through 
the unit of area of a plate of unit thickness in the unit of time 
when the flow of heat is steady, the difference in the tempera¬ 
tures of the sides of the plate being 1° C., is taken as the 
measure of the thermal conductivity of the substance of which 
the plate is composed, and is called its specific thermal con¬ 
ductivity. 

If the unit of length be one inch, and the unit of time 
one second, the thermal conductivity of a substance will be 
measured by the number of units of heat which flow in one 


A. 

ioo°C 












138 


MEASURE OF THERMAL CONDUCTIVITY. 


second across each square inch of a plate whose thickness 
is one inch when the temperature of one side is kept 1° C. 
above that of the other. If the difference of temperature 
be 10° C., the flow of heat will be 10 times this amount, and 
so on, while if the thickness of the plate be increased in any 
ratio, the flow will be diminished in the same ratio. 


215. The thermal conductivities of some bodies have 
been measured by determining how much ice can be melted 
in a given time through a plate of known area and thick¬ 
ness, when one side is kept in contact with boiling water. 


Suppose that a plate of wrought iron of 1 inch in thick¬ 
ness and 2 square feet in area is placed so as to form a 
division between water on the one side which is kept at 
12 ° C. and melting ice on the other side, and suppose that 
at the end of an hour we find that 164 pounds of ice have 
been melted. The amount of heat required to melt 164 
pounds of ice at 0° C. is about 12956 units : 

.'. in 1 hour through 288 sq. ins. of the plate, when the 
temperatures of its sides differ by 12° C., 12956 units of 
heat flow; 

.*. in 1 hour through 288 sq. ins. of the plate, when the 


temperatures of its sides differ by 1°C., 


12956 

12 


units of 


heat will flow; 


.*. in 1 hour through 1 sq. in. of the plate, when the 

temperatures of its sides differ by 1°C., units of 

12 x 288 

heat will flow; 


.*. in 1 second through 1 sq. in. of the plate, when the 

12956 

temperatures of its sides differ by 1°C., ^——— units 

±£ X Zoo X oOUU 

of heat will flow. 


The measure of the thermal conductivity of wrought iron 
referred to a second and an inch as units of time and space, 
the unit of heat being taken, as usual, to be the amount 
required to raise 1 lb. of water 1°C. from 0°C., is therefore 


12956 

12 x 288 x 3600 


* 001 .... 






EXAMPLES OF CONDUCTION OF HEAT. 


139 


This method however leads to very fallacious results in 
the case of metals and other good conductors, for the heat is 
transmitted through the substance of the plate far more 
quickly than it can be given up to the water. The hot water 
on the one side gives heat to- the metal, and the layer of water 
in contact with the metal becomes- cooled, while the heat is 
transmitted so rapidly through the metal that this layer 
becomes very much cooled before it can get away and be 
replaced by hotter water. Similarly, on the other side of 
the plate the layer of water close to the metal becomes 
heated, and receives heat so fast that its temperature is raised 
through several degrees hpfore the heated layer gives up its 
place to a colder one. Hence the water actually in contact 
with the hot face of the metal, and therefore the hot face of 
the metal itself, will be much below the boiling point, while 
the water in contact with the cold face, and therefore also the 
cold face itself will be much above the freezing point, so that 
instead of a difference of temperature of 100° C. between the 
faces of the plate it may happen that this difference is only 
3° or 4°. The measure of the conductivity obtained will 
therefore be far too small. With bad conductors, however, 
the method may lead to fairly accurate results. 

216. As another example we may find how much water 
at 100° C. can be evaporated per hour at atmospheric pres¬ 
sure in an iron boiler which exposes a surface of 20 square 
feet to the fire, supposing the iron to be J inch in thickness 
and the fire to keep its lower surface at a temperature of 
150° C. 

The thermal conductivity of iron being '001 referred to 
an inch and a second, it follows that the number of units 
of heat passing through the iron in an hour will be 
•001 x 2 x 144 x 20 x 3600 x 50, 
since the difference of temperature of its sides is 50° C.; and 
since the latent heat of steam is represented by 537, the 
number of pounds of water evaporated will be 
•001 x 2 x 144 x 20 x 3600 x 50 _ 

537 

or the quantity of water evaporated per hour will be about 
193 gallons. 



140 


EXAMPLES OF CONDUCTION OF HEAT. 


217. Most substances conduct heat equally well in all 
directions through their mass, but some 
crystals and organized structures conduct 
heat more readily in some directions than 
in others. Thus if a plate be cut from a 
quartz crystal parallel to its axis, covered 
with paraffin, and heated by a wire at the 
centre, the paraffin will be melted within an 
ellipse, whose major axis is parallel to the axis of the crystal, 
as shewn in fig. 39. This is due to the thermal conductivity 
of the crystal being greater in the direction of its axis than 
in any other direction. Paraffin^is preferable to wax for 
this experiment because it does not soften so much as wax 
before melting, so that the boundary between the solid and 
the liquid is much more distinct. 

If the plate of quartz be cut perpendicularly to the axis 
of the crystal the paraffin will melt in a circle, shewing that 
the thermal conductivity is the same in all directions at 
right angles to the axis of the crystal. 

218. In order to compare the thermal conductivities of 
wrought iron at different temperatures, Principal Forbes 
employed a bar about 10 feet in length and 1J inch square. 
One end of this was inserted into a crucible of lead, which 
was kept melted, great care being taken to preserve the 
temperature constant throughout the experiment. The rest 
of the bar was protected from the radiation of the lamp 
and crucible by means of a double screen. A number of 
small holes were drilled at intervals along the upper surface 
of the bar, and in these holes were placed the bulbs of small 
thermometers, the holes being filled up with mercury. The 
thermometers served to determine the form of the tempera¬ 
ture curve described in Art. 210. Then, knowing the form 
of this curve, and therefore the rate of change of tempera¬ 
ture at different points along the bar when the flow of heat 
became steady, it was only necessary to determine the amount 
of heat which flowed across any section of the bar, per 
second, in order to know the conductivity of iron at the 
temperature of the section. Now, as explained in Art. 208, 
when the flow of heat is steady the amount which crosses 
any section of the bar in each second is equal to the amount 




EXAMPLES OF CONDUCTION OF HEAT. 141 

radiated by the portion of the bar between that section and 
the cold extremity. Thus, referring to fig. 37, Art. 210, the 
amount of heat passing the section of the bar at S is equal 
to the amount radiated in the same time by the portion SE 
of the bar, since the temperature at every point of the bar 
itself remains constant. In order to determine the amount 
radiated, Principal Forbes employed a short length of wrought 
iron bar of the same section as the experimental bar, and 
having heated it to the temperature of the hottest part of 
the experimental bar he observed the rate at which it cooled 
by means of a thermometer inserted in a hole drilled in the 
bar. Knowing the specific heat of iron at different tempe¬ 
ratures, the rate at which heat escapes by radiation from 
each inch of the bar at temperatures varying from that of 
the room to that of the hottest portion of the experimental 
bar became known, and hence the amount lost, per second, 
by any portion of the experimental bar measured from the 
cold end, could be determined. This gave the flow of heat 
across any section, and consequently the absolute conduc¬ 
tivity, since the rate of change of temperature was known. 
The results of this investigation indicated that the conduc¬ 
tivity diminished as the temperature increased, changing 
steadily from *01337 foot-minute-degree units at 0°C. to 
*00801 units at 275°. A second experiment with a one-inch 
bar gave similar results, though in the latter case the differ¬ 
ence as well as the conductivity itself was less. 

219. By a method similar to that of Principal Forbes, 
but employing bars of different metals, Despretz determined 
the relative thermal conductivities of several metals, and 
Forbes’ apparatus is sometimes called after Despretz. In 
accurate determinations of the conductivity of metals the 
measurements should be conducted in vacuo, as air-currents 
help to accelerate uniform distribution of temperature. 

220. Wiedemann and Franz improved upon Forbes’ 
method by employing thin bars, or wires, one end of each of 
which was heated to a constant temperature, and the variation 
of temperature along the bar was determined by placing a 
thermo-electric junction in contact with the surface of the 
metal. This avoided the errors caused by drilling holes in 
the bar as in the experiments of Forbes and Despretz. The 


142 CONVECTION CURRENTS. 

relative thermal conductivities of some metals, as deter¬ 
mined by Wiedemann and Franz from experiments in vacuo, 
are given in the following table : 


Silver 

1000 

Iron 

10T 

Copper 

74-8 

Steel 

10-3 

Gold 

54-8 

Platinum 

9*4 

Brass 

240 

Lead 

7-9 

Tin 

15-4 

Bismuth (in air) 

1*8 


The conductivity of copper is very greatly diminished by 
small quantities of impurities. 

221. It is owing to the high conductivity of copper that 
a piece of copper gauze may be depressed upon a gas flame 
without any of the gas which passes through the gauze 
igniting above it. Similarly, if a piece >of fine copper gauze 
be held over a gas-jet and the gas ignited above the gauze, 
the flame will not be communicated to the gas below. In 
the gauze-burner the jet of gas mingles with the air as it 
escapes, and then, passing through a sheet of gauze, is ignited 
above it. The Davy safety-lamp consists simply of a gauze 
cylinder, in the interior of which the candle burns, but no 
flame can be communicated to any inflammable mixture 
outside the gauze. 

222. Pure copper and pure silver are the best con¬ 
ductors of heat known. Animal and vegetable substances 
are for the most part very bad conductors. Solids are in 
general very much better conductors of heat than liquids, 
while the thermal conductivities of gases are extremely 
small. Both liquids and gases are capable, however, of 
readily diffusing heat throughout their masses, since the 
extreme mobility of their parts makes up for their low con¬ 
ducting powers. Heat is therefore generally diffused through 
liquids and gases by convection. 

223. It is a well-known fact that there is an upward 
current of air above and around a gas-flame, because the 
air which has been heated by the flame is less dense than 
the rest of the air in the room. For a similar reason there 
is a draught up a chimney when a fire is burning below 
it. Now suppose a gas-flame burning in the middle of a 
room, the doors and windows of which are closed. There 
will then be an upward current of hot air in the middle of 


CONVECTION CURRENTS. 


143 


the room above the flame, while a downward current must 
exist nearer the walls in order to supply the place of the 
ascending air. In this way the air in the room will be 
kept in circulation, and heat will be conveyed from the gas- 
flame to other parts of the room by convection. The currents 
so set up are sometimes called convection currents. 


224. If a little cochineal be thrown into a 
vessel of water, and heat applied at the bottom, 
the water will be seen to circulate, an upward 
current being formed in the middle of the vessel 
immediately over the flame, while downward 
currents exist all round the circumference. In 
this way all the water is brought in turn close 
to the bottom of the vessel, where it is heated by 
conduction through the vessel itself, while the 
heated stream of liquid meeting, during its as¬ 
cent, with colder liquid, parts with some of its 
heat to the latter by conduction, and thus by a 
combination of the processes of convection and 
conduction the whole of the liquid becomes heated. 


Fig. 40 . 



It will be seen from the above that the rate at which a 
mass of fluid can be heated by a source of heat will depend 
on the position of the latter relative to it, and will generally 
be greatest when the heat is applied at the bottom of the 
fluid. 


When a quantity of fluid is being heated, convection 
currents serve to carry the hot portions of the fluid away 
from the source of heat and to bring the colder portion 
near to it, and also to mix together the hot and cold portions 
of the fluid, but the ultimate transfer of the heat to the 
colder portion of the liquid must take place by conduction. 
The mixing serves to bring .hot and cold portions very near 
together, and also causes them to present an immense area 
of surface of contact across which the heat may flow, and 
thus in two ways accelerates the uniform distribution of the 
heat, compensating in a great measure for the very low con¬ 
ducting power of most fluids. 

225. The low thermal conductivity of water may be 
shewn by placing a quantity of ice-cold water in a test-tube, 







144 


CONVECTION CURRENTS. 


and fixing a block of ice at the bottom. On heating the 
tube at about the middle point of its length, as shewn in 
fig. 41, the water above this point 
will be quickly heated by aid of 
convection currents, and may be 
made to boil before very much of 
the ice is melted, on account of the 
extreme slowness with which heat 
is conducted downwards to the ice, 
in which passage it is, after a short 
time, unaided by convection currents. 

The extreme slowness with which 
heat is conducted through water 
may also be shewn by placing a 
differential thermometer in a tall 
glass vessel of water, with one bulb about one inch below 
the surface, and the other as low down as possible. If a 
tin vessel containing water near its boiling point be held 
with its bottom just below the surface of the water in the 
glass vessel, a long time will elapse before the upper bulb 
of the thermometer becomes sensibly warmed. 

226. Let a glass tube be bent so as to form a rectangle, 
and the ends united so that it may be possible for water 
to circulate in the tube. At one corner let an opening be 
made and a small piece of tube sealed into the opening by 
which water may be poured into the apparatus. Now let 
the rectangle be supported in a vertical plane, and some 
coloured water be poured into the lower part of the tube, 
the rest of the tube being completely filled with uncoloured 
water. If the flame of a spirit-lamp be applied to one of the 
vertical sides the liquid will rise in this side and descend 
in the other, so that the coloured water will presently reach 
the top of the tube, then pass along the top branch and 
descend on the other side. The circulation will continue 
so long as the flame is applied, and after the colouring matter 
has become uniformly diffused the current may be rendered 
apparent by inserting a few solid particles, which will remain 
suspended in the water. 

227. It is by means of a circulation precisely similar 
to that described in the last Article that houses and other 


Fig. 41. 




CONVECTION CURRENTS. 


145 


buildings are generally heated by hot water. The glass 
tube is replaced by an iron pipe, a coil being inserted in 
the circuit wherever it is desired to expose a considerable 
heating surface. The boiler is generally placed in the 
lowest situation available. To ensure a rapid circulation 
it is essential that the outflow pipe for the hot water should 
leave the boiler at the highest point, and ttoat the return 
should enter at the lowest 
point of the boiler. It is best 
to carry the outflow pipe ver¬ 
tically upwards as far as pos¬ 
sible, so as to have a tall ver¬ 
tical column of water at the 
highest temperature of the 
circuit. The heavier water 
in the cold return pipe over¬ 
balances the hot column in 
the boiler and flow pipe, thus 
setting up and maintaining 
the circulation. A small tank 
is generally inserted at the 
highest point of the pipes, and connected with a feed cistern 
by which cold water is supplied to the apparatus when 
necessary. (Fig. 42.) 

Under ordinary circumstances it is desirable that as little 
water as possible should be drawn from a boiler or pipes 
employed in heating a building, for every addition of cold 
water generally brings with it a considerable amount of lime, 
salts, or other solid matters in solution and ’these are de¬ 
posited in the boiler and tubes when the water is heated. 
It is a great mistake to use a hot water heating apparatus 
as a source of hot water except where the ordinary water 
supply is particularly pure. 

228. Convection currents were employed by Dr Joule in 
order to determine the temperature at which the density of 
water is a maximum. Two vessels, 4 ft. 6 in. in height, and 
6 in. in diameter, were placed side by side and connected 
near their bases by a tube with a stop-cock, while an open 
trough served to connect them near their upper edges, a 
small piece being cut from the side of each. The vessels 

G. 10 



















146 


CONVECTION CURRENTS. 


were filled with water, and a small glass bead made to float 
in the connecting trough at the top. The temperature of the 
water in each was adjusted with the stop-cock closed. Then, 
on opening the cock, the water flowed through the trough, 
carrying the bead with it towards the vessel in which the 
density was greatest. If there were no current, the tempera¬ 
ture of the vessels being different, one was above and the 
other below the temperature corresponding to n&iximum 
density; and by finding a number of pairs of temperatures, 
for which there was no convection current, Joule concluded 
that the temperature corresponding to maximum density 
was about 39T°F. 




CHAPTER IX. 


ON RADIANT ENERGY. 

229. If we heat one end of a poker in the fire but not 
to redness, and then hold it near the face, a sensation of heat 
is at once felt, and we infer that some thing or some influence 
has passed from the poker to the face across the intervening 
air. If we now replace the poker in the fire and heat it to 
very dull redness, the same sensation is felt on bringing it to 
the same distance from the face, but in a stronger degree. If 
we now hold the poker in front of a black screen and look at 
the heated end through a prism, whose edge is parallel to 
the length of the poker, we see a dull red band slightly 
wider than the poker itself. If the edge of the prism be 
towards the left hand, the poker, when viewed through the 
prism, will appear more to the left than its true position. 
On heating it still further, till it attains a bright red heat, 
and again inspecting it through the prism, the red band will 
appear broader and brighter, and shade off into orange to¬ 
wards the left. On raising the temperature of the poker still 
more the red and orange become brighter, while yellow, green, 
blue and violet bands, gradually shading into each other, are 
successively added towards the left. When the violet has 
made its appearance the poker will have attained a white 
heat, and no more tints' visible to the eye will be added by 
further increasing the temperature, though the brightness 
of those already existing will be increased by this means. If 
the poker, at an intense white heat, be placed at a consider¬ 
able distance in front of paper prepared for receiving photo¬ 
graphic images, it will be found capable of blackening it, which 
will not be the case when the poker is red hot. 


10—2 


148 


RADIATION ANALYSED. 


The influence proceeding from the poker which produces 
the sensation of heat on the skin, or of light in the eye, or 
which is capable of blackening photographic paper, is called 
the radiation from the poker. As such radiation is capable 
of doing work it is frequently called radiant energy . 

230. Now let the following experiment be performed: 


A mass, B (fig. 43), of 
wrought iron or of platinum 
is heated to intense white¬ 
ness, and placed behind a 
double screen S, in which a 
narrow slit is cut, and a 
glass prism is placed in front 


Fig. 43. 


S 



of the screen with its edge \ 
parallel to the length of the 

slit. A coloured band BV I 

will then appear upon a cV' 

white screen placed in front \ 

of the prism, the end B to- \ 

wards the edge of the prism being red, and this will be suc¬ 
ceeded by orange, yellow, green, blue and violet towards 
the end V. If now a thermo-electric pile be moved from 
point to point of the coloured band, or light spectrum, the 
galvanometer connected with it will indicate that the face 
ttirned towards the prism is heated, and this will be the case 
even beyond the end B. If in like manner photographic paper 
be placed at different parts of the spectrum, it will be black¬ 
ened only in the blue and violet spaces, and in the space VG 
beyond the extreme violet. Let these observations be con¬ 
tinued while the mass of metal cools. We observe, first of all, 
that photographic paper made to pass across the spectrum 
between V and G is gradually less and less blackened, till at 
last it is quite unaffected, while the intensity of the light 
spectrum gradually diminishes. Th& light at the extreme 
end of the violet then vanishes completely, and presently the 
whole of the violet is gone, the blue follows, then the green, ajid 
so on, while the galvanometer registers a gradual diminution 
in intensity in the radiation at the red end of the spectrum 
and in the parts beyond the red. Before all the light spec¬ 
trum has vanished let the glass prism be replaced by a prism 






RADIATION ANALYSED. 


149 


of rock salt. The galvanometer will immediately indicate a 
great increase in the intensity of the radiation falling on the 
thermo-electric pile placed beyond the red end of the spec¬ 
trum, and will also indicate the presence of rays at much 
greater distances beyond the red than were indicated when 
the glass prism was used. As the metal, B, continues to cool, 
the green, yellow, and orange lights vanish in succession, and 
at last, when the metal is reduced below a red heat, the last 
trace of red vanishes. The galvanometer, however, continues 
to indicate the presence of radiation beyond the red end of 
the spectrum, though it now gives no indication of heat when 
the thermo-electric pile is placed in what was the illuminated 
portion of the spectrum, shewing that when the light vanished 
the rays capable of heating the junctions in the thermo¬ 
electric pile vanished with it. As the mass of metal becomes 
cooler we have to move the thermo-electric pile still farther 
from the red end of the original spectrum in order to get in¬ 
dications of radiation, and at length the metal becomes too 
cold to produce any sensible effect on the pile wherever 
placed. 

This experiment may be modified, so as to be more easily 
performed, by substituting an electric light for the white-hot 
metal, and an oil-lamp for the metal when at a bright yellow 
heat, a piece of metal being conveniently employed for lower 
temperatures, but this interferes with the continuity of the 
results*. 

In the solar spectrum the greatest intensity of the radia¬ 
tion, as measured by the thermo-electric pile, is a little be¬ 
yond the extreme red, while the greatest amount of radiation 
capable of affecting photographic paper is just beyond the 
extreme violet end of the luminous spectrum. 

231. From the experiments just described we learn that 
a solid body when heated below redness emits rays capable 
only of producing heat in bodies on which they fall, while at 
higher temperatures it emits rays capable of producing the 

* Instead of using a double screen as shewn in the figure it is much 
better to employ a thin screen and to place a lens of the same material as 
the prism between the latter and the slit in such a position that the slit is 
in its principal focus, a second lens of the same material being placed very 
close to the prism on the other side of such focal length that the second 
screen passes through its principal focus. 


150 


IDENTITY OF LIGHT AND RADIANT ENERGY. 


sensations of red, orange, yellow, green, blue, and violet light, 
while the intensity of the heat-producing rays is increased. At 
still higher temperatures it also emits rays capable of producing 
photographic pictures, but not causing the sensation of light. 

From this experiment we also infer that the same rays 
which produce the sensation of light in the eye, produce heat 
when allowed to fall upon other bodies, and hence we can 
make no distinction between light and, what has been er¬ 
roneously called, radiant heat. The same is true of the 
radiation which produces photographic effects, though the 
energy of these rays is generally too feeble to produce much 
current in the thermo-electric pile. 

232. If it be true that some of the rays which produce the 
sensation of heat are identical with those of light, since we 
cannot suppose that these rays essentially differ in kind from 
the other rays which produce the sensation of heat, but not 
that of light, we must conclude that the whole of the radia¬ 
tion which produces heat in bodies absorbing it is of the same 
nature as light, and therefore consists of vibrations of the 
luminiferous ether, and from the distribution of these rays over 
the luminous and non-luminous portions of the spectrum we 
are led to infer that the dark rays differ from one another 
and from the luminous rays in exactly the same way as 
the latter differ among themselves, that is, in wave-length, 
and that as the wave-lengths of the rays continue to increase 
as we pass along the spectrum from violet to red, so this in¬ 
crease continues beyond the red end. Hence bodies at a low 
temperature give out only those rays whose wave-lengths are 
very long compared with the length of a wave of light of any 
particular colour. Of the identity of the nature of calorific 
radiation and light we shall meet with further evidence shortly. 

233. Again, if it be true that all the rays which are 
capable of producing heat are of the same nature as light, 
we should expect that they would be subject to the same 
laws of reflection and refraction. In the experiments just 
described we have demonstrated the refraction of the dark 
rays by a prism. The reflection of these rays may be shewn 
thus:—Take a concave mirror, AB, fig. 44, and place at Q 
a small source of light; then the point q, at which the image 
of Q is formed by the mirror, can be readily determined. Now 


REFLECTION. 


151 


replace the luminous body at 
Q by a piece of metal heated 
just below redness, and place 
at q a delicate thermometer 
with a blackened bulb or a J 
thermo-electric junction con¬ 
nected with a galvanometer. 

The latter will immediately 
indicate a high temperature; 
but if it be moved from q to 
any other point at the same 
distance from Q no such effect 
will be produced, shewing that the dark radiation from Q, 
which falls on the mirror, is brought to a focus at q> and 
that therefore these rays are subject to the same laws of 
reflection as those of light. 

If two parabolic mirrors be placed opposite to one 
another so as to have the same axis, as in fig. 45, and the hot 

Fig. 45. 


*■ 

body be placed at Q, the focus of one mirror, while the 
thermometer is placed at q , the focus of the second, the dis¬ 
tance between the mircors may be very greatly increased 
without much diminishing the indication of heat by the ther¬ 
mometer. This follows from the fact that the rays pass from 
one mirror to the other, without sensibly heating the air; and, 
being all nearly parallel in their passage (if the body at q be 
small), nearly all the rays leaving the first mirror must fall on 
the second. 

If a luminous body, such as an oxy-hydrogen light, be 
placed at Q, and a quantity of finely powdered chalk or lime 



Fig. 44. 































152 


ABSORPTION. 


scattered through the air, the course of the light between 
the mirror and its accumulation in the neighbourhood of q 
will be distinctly visible. The same applies in the case of 
the lens mentioned below (Art. 239). 

234. The preceding experiments prove that the laws of 
reflection for other rays are the same as those for light, viz.:— 

(1) The incident and reflected rays are in one plane 
with the normal to the reflecting surface at the point of in¬ 
cidence, and on opposite sides of it. 

(2) The incident and reflecting rays make equal angles 
with the normal to the reflecting surface at the point of in¬ 
cidence. 

235. In the experiment described in Art. 229, we found 
that on substituting a rock-salt prism for the glass prism, 
the galvanometer indicated an increase in the radiation 
falling on the pile when placed beyond the red end of the 
spectrum. If similar pieces of polished glass and rock salt 
be exposed to the same radiation, especially if the greater 
part of it consist of dark rays (as is usually the case), the 
glass will become more highly heated than the rock salt. 
From these two observations we infer that glass absorbs 
much of the dark radiation which rock salt transmits, the 
glass being thereby heated. This is equivalent to saying 
that rock salt is more diathermanous than glass, although its 
power of transmitting luminous rays, or its transparency, is 
no greater than that of glass. All bodies absorb some of the 
rays incident upon them, that is, are opaque (or adiather- 
manous) to rays of certain wave-lengths. Metals are almost 
perfectly opaque to all rays. (Gold in exceedingly thin 
leaves transmits green light, and silver blue light.) All 
bodies absorb the same kind of rays which they themselves emit 
when heated. This accounts for the dark lines in the solar 
spectrum, and is the basis of solar and stellar chemistry. 
Thus sodium vapour absorbs the yellow rays corresponding 
to the double D line of the solar spectrum, and emits only 
these luminous rays when incandescent, so that it is im¬ 
possible to make sodium vapour white-hot. 

When a gas or vapour emits the same kind of light at 
very high temperatures and at comparatively low ones it is 


SELECTIVE ABSORPTION. 


153 


possible to reverse its spectrum by causing the light from the 
electric arc to pass through a Bunsen flame containing the 
substance in question. Black lines will then appear corre¬ 
sponding exactly to the bright lines which are visible when 
the Bunsen flame is removed and a small quantity of the 
substance placed in the electric arc. (The lines of course are 
not absolutely black, being illuminated by the light from the 
gas flame, but they appear black by contrast.) If the sub¬ 
stance in the electric arc produces bright lines which are not 
visible in the flame spectrum, these lines, of course, cannot be 
reversed by this method. The reversal of the bright lines in 
the spectra of metals or other substances is an example of the 
“ Theory of Exchanges.” 

236. The property of selective absorption is possessed in 
some degree by all known bodies however transparent. The 
clearest glass absorbs not only the non-luminous radiation 
beyond the visible end of the spectrum, but also absorbs 
nearly all the chemically active radiation which is more 
refrangible than the violet. In fact, it transmits very little 
radiation beyond that which is sensible to the eye. Many 
bodies which appear to be much less transparent than glass 
transmit more of the total radiation from the sun or the 
electric light. As above stated, rock-salt transmits nearly 
the whole of the ultra-red radiation; quartz, on the other 
hand, transmits rays lying very much beyond the violet, so 
that the spectrum of the electric light produced by quartz 
prisms and lenses can be traced to a distance beyond the 
extreme violet equal to three or four times the length of the 
visible spectrum. These rays may be rendered apparent 
either by their photographic effects, or by causing them to 
fall upon certain fluorescent substances, like sulphate of 
quinine, aesculine, &c., which absorb them and then shine 
with a visible light. 

237. The fact that glass absorbs so much of the non- 
luminous radiation which falls upon it, accounts for its effi¬ 
ciency as a fire-screen as well as its action in hot-houses. 
By far the greater part of the radiation from an ordinary 
fire is non-luminous, and this is absorbed by a glass fire¬ 
screen, rendering the screen itself warm, and then being 
radiated by the glass in all directions, so that the portion 


154 


SELECTIVE ABSORPTION. 


reaching any person in the room is much less than it would 
be if the screen were not present, while the cheerful lumi¬ 
nous radiation is nearly all transmitted. When glass is 
employed in frames and hot-houses a very large per-centage 
of the solar radiation is transmitted, since very much of it is 
luminous, but of the non-luminous radiation from the plants, 
earth, and other objects below the glass, nearly all is ab¬ 
sorbed by the glass, which returns through its own radiation a 
great portion of that which it absorbs to the objects beneath it. 
The glass thus acts like a trap or ratchet, allowing the radia¬ 
tion to pass in one direction, but refusing to allow it to return. 

Air which contains aqueous vapour acts like glass, ab¬ 
sorbing very much of the non-luminous radiation from the 
earth, &c., while it transmits the radiation of shorter wave¬ 
lengths from the sun. Air devoid of aqueous vapour is much 
more diathermanous to non-luminous radiation than air con¬ 
taining it. The same property of absorbing non-luminous 
radiation is possessed by olefiant gas in a very marked manner. 

238. The following table shews the per-centage of the 
total radiation from the four sources mentioned, which is 
transmitted by a plate of the several substances named, one- 
tenth of an inch in thickness. It will be noticed that rock- 
salt transmits with equal facility both luminous and non- 
luminous radiation, while Iceland spar, glass, tourmaline, 
selenite, alum, and ice, are almost opaque to radiation from 
a source at a low temperature. It is to Melloni we are 
indebted for these results. 


NAME OF SOURCE. 


Rock salt 

Locatelli 

Lamp. 

923 

Incandescent 

Platinum. 

923 

Copper at 
400° C. 

923 

Copper at 
100° C. 

92-3 

Fluor spar, 

72 

69 

42 

33 

Iceland spar, 

39 

28 

6 

0 

Glass, 

39 

24 

6 

0 

Quartz, 

38 

28 

6 

3 

Tourmaline (green) 

, 18 

16 

3 

0 

Selenite, 

14 

5 

0 

0 

Alum, 

9 

2 

0 

0 

Ice, 

6 

0 5 

0 

0 


The following table gives the relative absorbing powers 
of a few gases at a pressure of one inch of mercury, the 


LAWS OF REFRACTION. 


155 


length of the tube containing the gas being 2 ft. 8 in., and 
the source of radiation a plate of copper heated by a Bunsen 
flame. These results were obtained by Professor Tyndall. 

Absorption. 


Air, 1 

Oxygen, 1 

Nitrogen, 1 

Hydrogen, 1 

Chlorine, 60 

Carbonic oxide, 750 

Nitrous oxide, 1860 

Sulphuretted hydrogen, 2100 
Ammonia, 7260 

Olefiant gas, 7950 

Sulphurous anhydride, 8800. 


239. A solution of iodine in bisulphide of carbon ab¬ 
sorbs the whole of the luminous radiation from any source, 
while it transmits a large portion of the dark radiation. If 
a beam of solar light be brought to a focus in the air by 
a large achromatic lens and a wide vessel containing this 
solution be introduced into its path, the whole of the light 
will be cut off. (This Professor Tyndall proved by placing 
his eye so that the focus fell on the retina, defending all 
but the pupil by a perforated screen.) If now a small piece 
of platinum be placed at the point wdiich was occupied by 
the luminous focus, the platinum will be heated to white¬ 
ness, shewing that the dark rays are brought to a focus at 
the same point as the light by the. achromatic lens. (If a 
common lens be used, the best focus of these rays is a little 
beyond that of the red rays.) 

240. This experiment proves that dark radiation is 
subject to the same laws of refraction as light, viz.:— 

(1) The incident and refracted rays lie in one plane 
with the normal to the refracting surface at the point of in¬ 
cidence and on opposite sides of it, 

(2) In passing from one given medium to another , the 
sine of the angle of incidence hears a constant ratio to the sine 
of the angle of refraction , which depends only on the character 
of the radiation. 


156 


DOUBLE REFRACTION AND POLARISATION. 


Thus, if 10 represent a ray in¬ 
cident at 0 from air on a surface 
AB of glass and OR the refracted 
ray, NON' being normal to AB, 

ION is the angle of incidence and 
RON' the angle of refraction, and ^ 
if we make OR equal to 01 and 
draw IN, RN perpendicular to NN', 
the ratio of IN to RN is indepen¬ 
dent of the angle of incidence, and 
is called the index of refraction of 
the particular ray between air and glass. 

241. It is worthy of mention that when radiation passes 
through a considerable thickness of any particular medium 
the latter absorbs all the rays which it is capable of ab¬ 
sorbing, and the radiation may then be made to pass through 
another portion of the medium without being sensibly ab¬ 
sorbed by it. Thus if a beam of solar light be made to pass 
through a few inches of ice, it will melt the latter in the 
interior in the form of beautiful hexagonal flowers, like snow¬ 
flakes, whose planes coincide with the planes of freezing of the 
ice, but it may afterwards be made to pass through a lens of 
ice without damage to the latter, and may thus be brought 
to a focus in which platinum may be heated to redness. 

242. It is not only in reflection and ordinary refraction 
that non-luminous radiation obeys the same laws as light. 
It can also be doubly refracted by crystals and polarised. 
If light be allowed to fall upon a Nicol’s prism or a plate of 
tourmaline, all the vibrations of the transmitted light are 
reduced to one plane, the rest being absorbed by the tour¬ 
maline or totally reflected within the Nicol. If a second 
Nicol or plate of tourmaline be placed in the course of the 
light in one position the whole of the light will be trans¬ 
mitted, but if the second Nicol or tourmaline be turned at 
right angles to this the whole will be cut off. If a thermo¬ 
pile be placed in the course of the light it will be found 
that when the light is transmitted the pile is affected, but 
when the light is cut off no current is produced by the pile, 
shewing that all calorific radiation is cut off with the light. 


Fig. 46. 


N 

, J 


/ 

0 

B 

L 

f 


R 

AT 






LAW OF INVERSE SQUARES. 


157 


Hence the non-luminous radiation must be polarised by the 
first Nicol or tourmaline, and, in the case of the Nicol, this 
shews that it is also subject, like light, to double refraction. 

243. We see, then, that non-luminous radiation accom¬ 
panies light in reflection, refraction, double refraction, and 
polarisation, and is subject to precisely the same laws as the 
light itself. Hence we infer that it is of the same nature as 
light, that is, a vibratory motion of the luminiferous ether, a 
very rare jelly-like solid which is supposed to pervade the 
whole visible universe. By exploring the spectrum with the 
thermo-pile we learn (Art. 230) that in most cases the greater 
part of the radiation is less refrangible than red light, and the 
vibrations constituting it are therefore longer and less rapid 
than those of red light. Fluorescent bodies indicate that when 
the source is at a white heat, there is also emitted radiation 
more refrangible, and therefore of shorter wave-length, than 
violet light, but this generally has very little heating effect. 
We conclude that all the radiation from hot bodies is of the 
same nature as light, but that only that portion of the radia¬ 
tion whose period of vibration lies between certain • limits 
produces the sensation of light. These limits vary some¬ 
what with different human eyes, and there is no reason 
apparent why some animals should not possess eyes capable 
of being affected by the radiation from bodies far below a 
red heat, or even at ordinary temperatures, so as to see every 
thing clearly in a room perfectly dark to us, provided the 
temperature is above a certain point. 

Light and non-luminous radiation being thus identical in 
nature and obeying the same laws, all the propositions of 
optics are equally true for all heat producing rays. 

244. Through uniform media radiation is propagated in 
straight lines. 

Suppose radiation emitted 
from a very small body at A 
to pass through a rectangular 
hole in a fixed screen B , and to 
fall on a second screen C, which A 
is placed parallel to B. The 
whole of the radiation which 
passes through the hole in B will 


Fig. 47, 




==0 







158 


Leslie’s cube. 


fall on a rectangular area on C, and the area of this rectangle 
will be proportional to the square of the distance of the 
screen C from A. But wherever the screen G is placed, the 
amount of radiation which reaches it is the same, viz.:— 
that which passes through the hole in B. Therefore the 
amount of radiation which falls on each unit of area of the 
rectangle efgh varies inversely as the area of this rectangle, 
that is, inversely as the square of the distance of G from A. 
Hence the intensity of the radiation at any point varies 
inversely as the square of the distance of the point from the 
source. This is known as the law of inverse squares. 

245. If the direction of the screen G be changed so that 
it receives the radiation from A very obliquely, it will be 
seen that the area of G on which this radiation which passes 
through the hole in B falls, will be increased, and the 
amount of radiation falling on the unit of area will be cor¬ 
respondingly diminished. In this way it will be seen by 
the student who has read Trigonometry that the intensity of 
the radiation received by C is proportional to the cosine of the 
angle of incidence. 

246. We have said (Art. 206) that when heat is trans¬ 
mitted by radiation it may travel from one point to another 
without heating the medium through which it passes. That 
radiation will pass through air without sensibly heating it may 
be shewn by the following experiment:—Let a small piece 
of platinum be covered with lampblack and placed in the 
bulb of a differential thermometer. By means of a lens let 
some of the solar radiation be brought to a focus in the air 
within the bulb, care being taken that none of the rays fall 
upon the platinum. The liquid in the tube will give a very 
slight indication of heat (and this slight indication arises 
principally from the heating of the glass of the bulb and 
consequent heating of the air in contact with it), shewing 
that the air is not sensibly heated by the rays. Now let 
the lens be moved till the focus falls upon the platinum. 
The latter will be almost immediately heated to redness and 
will then heat the air around it, and the liquid in the tube 
will be rapidly driven towards the other bulb. 

247. Different surfaces possess different powers of ra- 


RADIATION AND ABSORPTION. 


159 


diation; this may be shewn by constructing a metal cube, 
polishing one side, leaving a second with a dead metallic sur¬ 
face, covering a third side with velvet or other material, 
and a fourth with lampblack. If the cube be filled with 
boiling water and its sides successively presented to the 
thermo-electric pile at a distance of, say, one foot, the galva¬ 
nometer will shew that the radiation is greatest from the 
side covered with lampblack, next greatest from the velvet 
side, and least from the polished side. This cube is called a 
Leslie’s cube. By covering its sides with different materials 
we may determine their relative radiating powers. 

Similarly, if two equal tin canisters be filled with hot 
water, and one expose its polished surface to the air, while 
the other is closely covered with flannel, the latter will cool 
more quickly than the former on account of the radiating 
power of the flannel. If the flannel do not touch the canister 
it will serve to keep in its heat. 

From these experiments we conclude that surfaces which 
reflect well radiate badly, while bad reflectors are good radiators . 

Again, if the bulb of a thermometer, or face of a ther¬ 
mo-electric pile, be covered with lampblack, it will absorb 
radiation incident upon it much more readily than if it be 
kept clean. A quantity of water can be boiled in a kettle 
whose exterior has been blackened, much more readily than 
in a similar kettle kept bright. Combining these results with 
those of the experiments just described, we infer that sur¬ 
faces which reflect well both radiate and absorb badly , while 
surfaces which are bad reflectors are good radiators and also 
absorb a large portion of the radiation incident upon them. 

We may mention that the absorbing power of any surface 
is generally different for the radiation from different sources. 
Lampblack absorbs nearly all the radiation incident upon it 
from any source, and for this reason the bulb of the ther¬ 
mometer, or face of the thermo-electric pile, employed to 
measure radiation, should be covered with lampblack. The 
radiation emitted by any body always increases as the tem¬ 
perature of the body is raised. 


248. The difference between the absorbing power of a 
bright metallic surface and of a blackened surface can be conspi- 


ICO 


RADIATION AND ABSORPTION. 


cuously shewn by the ap¬ 
paratus sketched in fig. 48, 
in which A and B repre¬ 
sent two discs of tinned 
iron to the backs of which 
are soldered small bars 
of bismuth, (7andZ>. The 
disc A is bright, but B 
is covered with lamp¬ 
black. The discs are 
united by a copper wire 
AB , and the bismuth 
bars are connected with the electrodes of a galvanometer, G. 
A red-hot iron ball E is placed midway between the discs. 
Now, if the junction of the bismuth bar, D , with the iron 
plate, B, only be heated, an electric current will pass from the 
bismuth to the iron across the hot junction, and so go through 
the galvanometer from C to D. If the junction of A and G 
alone be heated the current will go through the galvano¬ 
meter in the opposite direction, while if both junctions be 
heated equally no current will be produced. After intro¬ 
ducing the hot ball between the plates it is found that the 
current passes through the galvanometer from G to D, indi¬ 
cating that the junction of the bismuth with the blackened 
plate B is more heated than the other, whence we infer that 
the plate B absorbs more radiation than the bright plate A. 
By removing B farther from the source of heat we can find 
a position for B in which no current passes, and then, com¬ 
paring the distance of A and B from E } can calculate approxi¬ 
mately the relative absorbing powers of the two surfaces. 
In one experiment when the hot ball was midway between 
the plates the solder uniting the bismuth bar to the blackened 
disc was melted and the bar dropped off while that on the 
bright disc remained perfectly sound. 

249. If some letters be written in ink on a piece of 
platinum foil, on heating the foil to redness a little oxide of 
iron is left clinging to the platinum. If the foil be now 
heated in a Bunsen flame in a dark room the letters will 
appear much brighter than the rest of the foil, shewing that 
the iron oxide, which reflects much less light than the 


Fig. 48 . 








RADIATION AND ABSORPTION. 


1G1 


platinum, radiates much more when incandescent. Now 
let the platinum be turned over in the flame so that the 
plain side may be seen. The letters will still appear legible 
(though inverted), but in this case the letters appear dark 
on a bright ground. The reason of this is that more radia¬ 
tion being emitted from the iron oxide than from the pla¬ 
tinum, the metal is cooled where the letters are written 
more than elsewhere, and the reverse side presenting every¬ 
where a uniform surface of platinum the amount of radia¬ 
tion emitted depends only on the temperature of the metal, 
and is therefore less behind the letters than elsewhere. 

250. We have stated (Art. * 247) that the radiation 
emitted by a hot body increases as the temperature rises. 
The amount which it receives depends of course upon the 
temperature of surrounding bodies, and if it be placed in 
an enclosure of uniform temperature below that of the body, 
the rate at which it will lose heat will depend on this differ¬ 
ence. Newton came to the conclusion that the rate of cooling 
is proportional to the excess of the temperature of the body 
over that of the enclosure. This result is known as Newton’s 
law of cooling, but is not strictly true. Dulong and Petit 
investigated the rate of cooling, both in air and in vacuo, 
of a thermometer bulb which was placed in the interior of a 
thin copper sphere, the sphere being- immersed in water 
at a known temperature. Their results indicate that the 
rate of cooling depends upon the absolute temperature 
both of the body and the receiver, and not simply upon their 
difference. For the same difference of temperature, the 
rate of cooling increases with the temperature of the 
enclosure. Thus, the difference of temperature being 100°, 
the rate of cooling when the enclosure was at 80° C. and 
the thermometer at 180° C., was 1*87 times the rate when 
the enclosure was at 0° aud the thermometer at 100° C. 

Dulong and Petit found that the rate of cooling of a body 
in vacuo in an enclosure at uniform temperature might be 
represented by the formula 

m(a t+9 -0L e \ 

where 6 represents the temperature of the enclosure and t 
the excess of the temperature of the body over that of the 


162 


THEORY OF EXCHANGES. 


enclosure. They also found the value of a to be 10077. 
The value of m depends on the body and enclosure concerned. 

This formula suggests the idea that the loss of beat of 
the body to the enclosure is represented by moi. t+0 and its gain 
from the enclosure by ma 0 , so that each increases in geometri¬ 
cal progression as the temperature increases arithmetically, 
but these quantities may be represented by ma t ' ]r0 + k and 
mo 0 + k respectively, where k is a constant which is the same 
for each. 


Theory of Exchanges. 

251. If in the focus of one of the conjugate mirrors 
described in Art. 233 we place the bulb of a thermometer, 
while a block of ice is placed in the focus of the other, the 
thermometer will indicate a decrease of temperature. The 
same would happen if the thermometer were placed in a 
cavity in a block of ice without touching the latter. The 
reason of this is that the thermometer emits more radiation 
to the ice than it receives from it. If the thermometer be 
placed in a room whose walls, as well as everything in the 
room, are at the same temperature as the thermometer, the 
latter will indicate no change; while if the thermometer 
be originally at a lower temperature than the room, its 
temperature will increase; if, on the other hand, it be at a 
higher temperature than that of the room its temperature 
will decrease. The behaviour of the thermometer in all 
these cases is completely explained by Prevost’s Theory of 
Exchanges. 

This theory asserts that every body radiates at a rate 
depending only on the nature and temperature of its surface, 
while it absorbs a certain fraction of the radiation it receives 
from other bodies, which fraction is a measure of the ab¬ 
sorbing powder of its surface for the particular kind of radia¬ 
tion which it receives. 

252. From the fact that a surface appears equally bright 
in whatever direction it is viewed it follows that 

The amount of radiation emitted by any surface is greatest 
in the direction of the normal to the surface , and that for 


THEORY OF EXCHANGES. 


163 


other directions the amount is proportional to the cosine of the 
angle which the direction makes with the normal. Also we 
have seen (Art. 244) that 

The intensity of radiation at any point varies inversely 
as the square of its distance from the source. 

From these data it may be shewn geometrically that if 
two bodies, A and B , which emit the same amount of radia¬ 
tion per unit of area of their surfaces, be placed near to each 
other, the amount of radiation reaching A from B is equal to 
the amount from A which falls on B. 

Suppose a thermometer to be placed with its bulb at 
the centre of a hollow sphere, which is initially at the same 
temperature as the thermometer, and any part of whose 
surface is capable of radiating ten times as much as an equal 
portion of the surface of the thermometer bulb at the same 
temperature. Experiment shews that the thermometer 
always retains the temperature of the enclosure in which it 
is placed. Suppose also that the surface of the sphere 
absorbs one-half of the radiation which falls upon it from 
the thermometer, the other half being returned to the ther¬ 
mometer by reflection. Then if the surface of the sphere 
radiated as much per unit of its area as that of the thermo¬ 
meter, just as much radiation would reach the thermometer 
from the sphere as the thermometer itself gives out; for, 
while the whole of the latter reaches the sphere, only a very 
small part of the radiation from the parts of the sphere 
reaches the small bulb at its centre, viz. that part of the 
radiation which leaves the surface of the sphere along the 
radius, or nearly in that direction. But since the sphere 
radiates ten times as much per unit of area as does the ther¬ 
mometer bulb, it follows that ten times as much radiation 
reaches the thermometer from the sphere as reaches the 
sphere from the thermometer; and since the thermometer 
retains the same temperature, and no heat can be lost .by it 
except by entering the sphere, it follows that in each 
second the thermometer must absorb the same amount of heat 
from the sphere as the sphere absorbs from the thermometer. 
But the sphere absorbs half of the total radiation from the 
thermometer. Therefore the thermometer must absorb one- 
twentieth of the radiation which reaches it from the sphere 

11—2 


164 


THEORY OF EXCHANGES. 


Hence while the spherical surface absorbs one-half of the 
total radiation from the thermometer, the latter absorbs but 
one-twentieth of that which it receives from the sphere, 
or the absorbing powers of the two surfaces are directly 
proportional to their radiating powers. Now whatever be 
the nature of the surfaces of the sphere and thermometer, 
the latter will always retain the temperature of the former; 
hence we conclude that if we measure the absorbing power 
of a surface by the ratio of the amount of radiation it absorbs 
to the whole amount incident upon it, 

The absorbing power of any surface , A, for radiation 
emitted from any other surface, B, is to the absorbing power 
of B for radiation reaching it from A, as the radiating power 
of A is to that of B. 

This relation is true not only of the whole radiation from 
the surface but also of any selected constituent thereof. 

253. As we have stated above, it may be shewn by 
geometry that if two bodies A and B, which emit the same 
amount of radiation per unit of area of their surfaces, be 
placed near each other, the amount of radiation from B which 
falls on A is equal to the amount from A which reaches B. 
Hence if any number of bodies, all at the same temperature, 
be placed in the neighbourhood of one another, each will 
emit radiation to, and receive radiation from, all the others, 
and the amount of radiation from any body B which any 
other body A absorbs, is exactly equal to the amount of 
radiation from A absorbed by B. 

Now suppose that two bodies A and B are near to each 
other, and the temperature of B is higher than that of A ; 
also suppose that the surface of B has ten times the 
radiating power possessed by A, and therefore ten times 
the absorbing power; and moreover that B absorbs half 
the radiation falling upon it from A. Then, by what we 
have proved, A will absorb one-twentieth of the radiation 
reaching it from B. But since B is at a higher tempe¬ 
rature than A, more than ten times as much radiation 
reaches A from B (of which A absorbs one-twentieth) as 
reaches B from A (of which B absorbs one-half). Hence 
A absorbs more radiation from B than B absorbs from 


THEORY OF EXCHANGES. 


165 


A , and thus the temperature of A rises while that of B 
falls. Thus if A be a block of ice, and B a thermometer 
originally at 15° C., and everything else in the room in¬ 
cluding the walls be at 15° C., the temperature of the 
thermometer will fall on account of the presence of the 
ice, while if the ice be removed the thermometer is capa¬ 
ble of receiving radiation from the wall, in the directions 
previously subtended by the ice, and thus its temperature 
wall be again raised to 15° C. and kept there. 

The following is a brief summary of our results. 

254. Prevost’s Theory of Exchanges may be thus stated: 

Every body emits radiation in all directions at a rate 
depending only on its temperature and the nature of its 
surface , while it absorbs radiation from all bodies to which it 
is exposed. 

Combining this with the known fact that a body placed 
in an enclosure kept at constant temperature acquires the 
temperature of the enclosure, we see that the following law 
must be true, viz.:— 

The absorbing power of any surface , A, for radiation 
emitted from any other surface , B, is to the absorbing power 
of B for the radiation from A as the radiating power of 
A is to that of B; the absorbing power of a surface being 
measured by the ratio of the radiation it absorbs to the whole 
radiation incident upon it. 

* The absorbing powers of any surface for rays of dif¬ 
ferent wave-lengths are proportional to its radiating powers 
for the same rays. 

255. When radiation falls upon a transparent, or dia- 
thermanous body, as rock-salt, or air, part of the radiation 
is absorbed within the body, and the absorption goes on as 
the radiation traverses it until all those particular rays which 
it is capable of absorbing have been filtered out, and the re¬ 
maining radiation is then transmitted by the body without 
sensible diminution (Art. 241). On examining the spectrum 
of radiation after traversing such a medium it will be found 


1G6 


CONSTITUTION OF FLAME. 


to be crossed by a Dumber of absorption bands, the radiation 
corresponding to which has been removed, leaving black spaces 
in the luminous portion of the spectrum, spaces in which a 
thermo-electric junction is unaffected in the parts beyond the 
red, and spaces in which photographic paper is unblackened 
beyond the violet. If the body be heated so as to become 
self-luminous it will be found that it emits those rays which 
in the previous case it absorbed. 

256. Not only is it true that bodies (including gases) 
absorb radiation of the same wave-length as they themselves 
emit, but if a body absorb radiation which is polarised in 
one particular plane, the radiation it emits when self-lumi¬ 
nous will be found polarised in the same plane. Thus a 
crystal of tourmaline absorbs all vibrations perpendicular 
to its axis, transmitting only those parallel to its axis. If 
such a crystal be heated to redness and the radiation 
examined through another crystal of tourmaline, or a Nicol’s 
prism, the vibrations will be found all to take place in 
the plane perpendicular to the axis of the crystal. 

257. Flame consists of gases heated so as to become self- 
luminous. Now gases (as we have seen in the case of air in 
Art. 246) possess very little power of absorbing radiation, and 
consequently possess very little power of emitting it. Hence 
a flame which contains within it no solid particles generally 
emits very little light. The flame of hydrogen burning in 
air or pure oxygen is scarcely visible in ordinary daylight, but 
if a piece of lime be heated by it we obtain the oxy-hydrogen 
lime light. When the pressure under which gases are burn¬ 
ing is very much increased, and their density consequently 
increased, they give out much more light than under ordinary 
circumstances. 

258. The radiation from an ordinary gas or candle flame 
is due principally to the presence of solid particles of carbon 
within it, and the illuminating power of coal gas depends on 
the amount of carbon it contains. An ordinary candle, or 
coal-gas, flame consists of three distinct portions. The cen¬ 
tral portion, A , fig. 49, called the area of non-combustion, 
contains gas which has not yet met with air, and is there- 


CONSTITUTION OF FLAME. 

fore not burning, and being at a comparatively 
low temperature is non-luminous. Surround¬ 
ing this area is another in which the gas has 
met with a partial but insufficient supply 
of oxygen, and in it a portion of the gas is 
burned while solid particles of carbon formed 
by its decomposition are raised to a very in¬ 
tense heat and emit much radiation. This 
is called the area of partial combustion and is 
marked B in the figure. Beyond this is the 
area of complete combustion, C, in which the 
particles of carbon are burned up, and since this area con¬ 
sists only of heated gas it emits very little radiation, although 
it is the hottest part of the flame. 

If the gas be mixed with air before being ignited, as in 
the flame of a Bunsen or gauze burner, the solid particles of 
carbon do not exist in it for a sensible time, and very little 
radiation is emitted. If the hand be held by the side of a 
Bunsen flame and the supply of air be suddenly cut. off so 
as to make the flame bright, the sensation of heat experienced 
by the hand will be at once very sensibly increased. 

259. In 1871 Mr Crookes discovered that when radiation 
was received by a body in an almost perfect vacuum it had 
a tendency to move in a direction opposite to that from which 
the radiation came, that is, to recede from the source of ra¬ 
diation. In his first experiments a small light body, such as 
a piece of elder pith, was attached to each end of a straw 
through the middle of which half a needle, pointed at both 
ends, was passed, and the straw was supported in a horizontal 
tube upon the points of the half needle, which was a little 
shorter than the diameter of the tube. The balance was 
effected by heating the heavier end so as to dry it. When 
the tube was exhausted by a mercurial air-pump it was at 
first found that a hot body appeared to attract the end of the 
straw near to which it was placed, but when the exhaustion 
reached a certain stage, which was different for different 
bodies balanced on the straw, the attraction ceased and re¬ 
pulsion set in. This repulsion was not due to currents of air, 
because it took place equally whether the hot body was 
placed below or above the straw. On substituting a piece of 



168 


THE RADIOMETER. 


ice for the hot body the ice appeared to attract the end of the 
straw near to which it was placed. 

260. Mr Crookes thus found that if pieces of metal were 
balanced on a straw the repulsion was greater when they 
were covered with lampblack than when polished, and that 
generally the repulsion was greater the greater the absorb¬ 
ing power of the surface. From this it would follow that 
if a disc of metal were polished on one side and covered 
with lampblack on the other and were exposed to radiation 
equally from all directions (as in diffused daylight), it would 
tend to move in the direction of the normal to its surface 
drawn outwards from its polished side, that is, the polished 
side would always appear to advance and the black side to 
retire. Upon this principle Mr Crookes constructed the 
Radiometer , a modification of which is shewn in fig. 50. 

It consists of a glass vessel into the bottom of which 
is sealed a tube, which is drawn off at the top and carries 
a sharp steel point. On this rests a light 
glass cup, A, which carries four vertical 
discs of aluminium at the extremities of 
horizontal arms at right angles to each 
other. The discs are thus supported on 
a bearing similar to that of an ordinary 
compass needle. A very narrow glass 
tube attached to the top of the vessel 
prevents the cup from falling off the point 
if the instrument be inverted. The 
vessel is exhausted through the tube 
BC , in which a hole D has been formed 
for this purpose, and the end of the tube 
is then sealed. The discs are covered 
with lampblack on one side only, and are 
arranged in order, so that the black sides 
all point in the same direction round a 
horizontal circle. From what has been 
said it will be seen that, with this ar¬ 
rangement, the arms carrying the discs will rotate when the 
latter are exposed to radiation, in the direction in which 
the polished faces look, in the same way as the arms of 
an anemometer carrying Robinson’s cups rotate in the direc- 


Fig. 50 . 














THE RADIOMETER. 


160 


tion in which the convex surfaces of the cups look. The rate 
at which the arms revolve may be taken to indicate the in¬ 
tensity of the radiation to which the instrument is exposed, 
and hence its name. 

261. It appears at first sight as if the action of the 
radiometer might be due to the impact of material particles, 
and thus seem to favour the corpuscular theory of radiation; 
but were the corpuscular theory true, the pressure on the 
polished surfaces at which reflection takes place, and from 
which the particles must therefore rebound, would be greater 
than that upon the blackened surfaces, which must retain 
them, and the arms would revolve in the direction opposite 
to that in which they actually move. 

262. Perhaps the best explanation hitherto given of 
the repulsion produced by radiation is that due to Professor 
Osborne Reynolds, of which the following is a brief sketch. 

Although a very good vacuum may have been produced 
within the receiver, there are always present some particles 
of air, or other gas, which, according to the dynamical theory 
of gases, are moving about in all directions, with velocities 
which increase with the temperature, and which exert pres¬ 
sure upon any surface exposed to their impacts. Now the 
surface of any body exposed to radiation becomes heated 
thereby, and the more so as its absorbing power is increased. 
Hence in the radiometer the blackened sides of the vanes 
become heated more than the polished sides. When the 
particles of air strike the surface, they rebound with veloci¬ 
ties which on the average are greater than those with which 
they strike it if the temperature of the surface be higher 
than that of the enclosure, and thus act like elastic balls 
whose coefficient of elasticity is greater than unity. The 
greater the velocity with which they rebound, the greater is 
the pressure they exert on the surface, and this pressure will 
therefore be greater the higher the temperature of the 
surface. The pressure of the air on the side of a body 
exposed to a source of radiation will therefore be greater 
than that on the opposite side, and the body will consequently 
appear to be repelled by the source; while in the radiometer 
the pressure of the air on the blackened faces will be greater 


170 


THE RADIOMETER. 


than that on the polished faces, because their temperature is 
higher, and the arms will therefore rotate in the direction in 
which they are observed to move. 

263. If the radiometer be exposed for some time to a 
high temperature, so as to heat the vanes considerably above 
the temperature of the air in the room, and be then al¬ 
lowed to cool, the blackened sides of the vanes will cool 
most readily, being better radiators than the other sides, 
and the bright sides being thus left at the higher tem¬ 
perature, the vanes will rotate in the opposite direction to 
that in which they move when exposed to sunlight in the 
usual way. By concentrating sunlight by a lens on the 
vanes they rotate rapidly, the black sides retiring ; then on 
removing the instrument into the shade the rotation ceases 
and presently commences in the opposite direction. 

264. By employing iron vanes and floating the instru¬ 
ment in water, while the vanes were held stationary by mag¬ 
nets, Dr Schuster found that the glass bulb rotated slowly 
in the opposite direction to that in which the vanes tended 
to rotate, thus shewing that the stresses producing the 
motion were not between the vanes and the source of light, 
as would be the case if the light acted directly upon the 
vanes, but both action and reaction were confined to the 
instrument itself. 

Clerk Maxwell in 1879 gave a very complete mathemati¬ 
cal investigation of the action of the radiometer, explaining 
why the vanes do not turn until the pressure of the air in 
the instrument is reduced below a certain limit. 


CHAPTER X. 


meteorology. 

265. We have now to consider the application of some of 
the experimental results we have obtained to the explanation 
of natural phenomena. We have seen that if air be heated 
without increasing the pressure to which it is exposed it ex¬ 
pands considerably* Hence hot air will rise in cold air on 
account of the action of gravity. Now during a hot day the 
sun heats the surface of the land and of the sea, but owing to 
cooling by the evaporation of the latter, and communication of 
heat to the water below on account of the continual movements 
of the sea, while the land is for the most part a very bad con¬ 
ductor of heat, the surface of the sea, and consequently the 
air in contact with it, becomes much less heated than that of 
the land. The air above the land being therefore more 
highly heated than that over the sea will ascend, and air 
from the sea will flow in to occupy its place, forming a sea 
breeze. 

During the night the land parts with its heat by radiation 
and becomes much more cooled than the sea, on account of 
the low radiating power and high specific heat of the latter. 
The wind then blows from the land to the sea, since the air 
above the sea ascends, thus forming during the night a land 
breeze. 

266. The equatorial regions of the earth become highly 
heated by the sun, which is vertical, or nearly so, in these 
regions at noon. The air there becomes consequently less 
dense than that in the adjoining temperate zones, and there¬ 
fore ascends to give place to the colder air, which, under 
the action of gravity, flows in from North and South, thus 


172 


TRADE WINDS. 


# 


tending to produce a North wind on the borders of the tem¬ 
perate and tropical zones in the Northern Hemisphere, and a 
South wind in the corresponding regions of the Southern 
Hemisphere. Now the surface of the earth near the equator 
has a velocity from West to East of more than a thousand 
miles an hour, on account of the earth’s rotation, while places 
in higher latitudes have a less velocity. As the air, then, 
flows towards the equatorial regions it is continually reach¬ 
ing places which have a greater velocity from West to East 
than those from which it comes, and, since it cannot im¬ 
mediately acquire this velocity, it has always a motion from 
East to West relative to the place over which it passes. Com¬ 
bining this with its previous motion towards the equator 
we get a North East wind in the Northern Hemisphere and 
a South East wind in the Southern Hemisphere. These are 
the trade winds. 

267. Now the air which ascended at the equator must 
come down somewhere to take the place of the air which 
flowed towards the equator from higher latitudes and make 
room for the air which continues to rise at and near the 
equator. This current of air on reaching the earth’s surface 
has, of course, a motion towards the nearer pole, but since it 
comes from places whose motion, on account of the rotation 
of the earth, is greater than those to which it is travelling, it 
will always have a velocity relative to these latter places in 
the direction in which the earth is turning, that is, from 
West to East , and combining this motion with its motion to¬ 
wards the pole we get a South West wind in the Northern 
Hemisphere and a North West wind in the Southern Hemi¬ 
sphere. These are the Counter Trades. 

268. On account of the great amount of heat absorbed 
by water in evaporating, the presence of a large quantity of 
water will have a great effect in moderating the excessive 
heat of the climate in summer, and its high specific heat 
enables it to give out so much heat while being cooled in 
winter as to considerably alleviate the cold in that season. 
The great equatorial current which (probably partly driven 
by the trade winds) has a motion from east to west in 
the Atlantic Ocean, and rushing into the Gulf of Mexico 


CLOUD. 


173 


washes round its shores, and then crosses the Atlantic as the 
Gulf Stream, has much to do with moderating the winter 
temperature in the north-west of Europe. Places in central 
Asia and North America in the latitude of London ex¬ 
perience excessive cold in the winter. The latitude of 
Moscow is not far different from that of Edinburgh. 

269. We have seen that if air be allowed to expand, by 
diminishing the pressure upon it, without allowing it to 
receive heat, it becomes cooled. Now, if the air be originally 
saturated with aqueous vapour, the diminution of the pres¬ 
sure which the vapour can exert on account of the decrease 
of temperature proceeds faster than the diminution of the 
pressure which it would have to exert on account of the 
expansion of the air if it all remained as vapour. Hence, as 
the air expands, some of the vapour must be condensed. In 
this way a cloud is formed in the receiver of an air-pump 
as the exhaustion proceeds. 

Consider an ascending current of air nearly saturated 
with aqueous vapour. As it ascends it becomes cooled, and 
soon the vapour within it is no longer able, notwithstanding 
its expansion, all to exist as vapour, and a portion of it con¬ 
denses, forming a cloud, which consists of drops of water, so 
small that the resistance offered to their motion by the air 
is sufficient to prevent their falling through it except with 
an exceedingly small velocity. The cloud seen to form in 
front of the spout of a tea-kettle containing boiling water, or 
above the safety-valve of a steam boiler, consists of small 
drops of water, and not of steam which is invisible. In the 
case of a kettle in which the water boils violently there is 
true steam which is invisible for some distance in front of 
the spout. 

270. Cloud may also be formed by a warm wind blowing 
against the side of a cold mountain. Here the wind is 
cooled by actual contact with the mountain, as well as 
by having to ascend its sides and so expanding under 
diminished pressure. As the air leaves the mountain the 
cloud sometimes evaporates, so that there appears to be a 
stationary cloud around the mountain top notwithstanding 
the presence of a strong wind. The cloud is, however, con¬ 
tinually being bloVn away and renewed. 


174 


CLOUD AND RAIN. 


From this we should expect mountains to exert a great 
influence on the condensation taking place in their neigh¬ 
bourhood, and it is a matter of observation that the rainfall 
in mountainous districts is, other things being the same, 
much greater than on extensive plains, while the districts 
lying to leeward of lofty ranges are sometimes rainless. 

271. Another cause of condensation is the mingling of 
currents of air at different temperatures. The pressure 
which aqueous vapour can exert at the mean of two tem¬ 
peratures is considerably less than the mean of the pressures 
it can exert at those separate temperatures, and conse¬ 
quently when two quantities of air at different temperatures 
mix, if each be originally saturated with aqueous vapour 
a portion of this must be condensed. 

Thus the greatest pressure of aqueous vapour at 5°C. is 
about *257 in. of mercury, while at 15°C. it is about *5 in. 
The mean of these is *3785 in., but the greatest pressure 
of aqueous vapour at 10° C. is only *36 in. Now suppose 
two equal masses of air, saturated with aqueous vapour at 
the temperatures of 5°C. and 15°C. respectively, to mix. 
The temperature of the mass will then be reduced nearly 
to 10°C., and consequently a portion of the vapour will 
be condensed till its pressure is only *36 in., instead of 
•3785 in., or about 5 per cent, of the whole amount of vapour 
in the two masses of air will be precipitated to form cloud. 
During this condensation the vapour which is condensed 
gives up to the air the latent heat of evaporation, thus 
preventing it from being cooled quite to the mean of the 
two temperatures, and also diminishing accordingly the 
amount of precipitation. 

In all these cases cloud is formed by the cooling of the air 
below the dew-point. 

When a cloud is formed near the surface of the earth, 
it forms a fog or mist. 

272. When some of the small drops of water in a cloud 
unite to form larger drops, they fall more rapidly than the 
others, and meeting with the small drops as they fall through 
the cloud, they attach themselves to theih, thus increasing 


HAIL, SNOW, AND DEW. 


175 


their own hulk and in consequence falling more rapidly. 
The union of the small drops of water of a cloud or fog thus 
produces rain. 

The very great amount of evaporation taking place in 
the equatorial regions, and the strong upward current of 
air there produced, account for the enormous rainfall in 
those parts. 

273. If, as the small raindrops fall, they pass through 
colder regions of the atmosphere, they become frozen, and 
thus fall as hail. Different opinions are, however, held with 
regard to the mode of formation of hail. 

If a cloud exist at a temperature below 0°C., or be 
formed by the mingling of a quantity of warm air with 
air so cold that the temperature of the mixture is below 
0°C., the condensed vapour will consist of minute crystals 
of ice. It is these small ice crystals which form halos round 
the moon on cold nights, and sometimes, especially in the 
early morning, produce beautiful halos round the sun. .The 
union of these small cryscals produces snow flakes, which 
grow as they descend by the aggregation of other crystals 
to their exterior. 

We have stated (Art. 140) that water may under special 
circumstances be cooled below 0°C. without freezing. Now 
and then this happens to raindrops which fall as water, 
but as soon as they meet with any disturbing body they 
congeal, forming a solid sheet of ice over the surface of an 
umbrella, or any other body on which they may fall, although 
its temperature may have been initially above 0°C. 

274. The earth in any locality emits radiation at a 
rate depending upon the nature and temperature of its 
surface. During the day it receives radiation from the sun, 
but during the night this is not the case, and a fall of 
temperature is the result. If the night be cloudy, the clouds 
radiate to the earth almost as much heat as they receive 
from it, so that its temperature is not much reduced; but 
if the night be clear, the surface of the earth radiates into 
space, and receiving nothing in return, a cold night is the 
result. The air very close to the earth, then, frequently 
becomes cooled below the dew-point, especially if the day 


176 


DEW AND HOAR-FROST. 


has been warm, and a white mist is seen to cover the 
land, particularly where grass, or the like, is growing. This 
mist deposited on the surfaces of the earth, of plants, &c., 
is dew. 

Very much more dew is deposited on grass and similar 
vegetable structures than upon the bare earth, or stones. 
The reason of this is that the blades of grass are exceed¬ 
ingly good radiators, but very bad conductors of heat; they 
therefore become intensely cold, and the air around them 
being cooled by contact, deposits very much of its moisture 
upon their surfaces. Stones and the like are not such 
good radiators as blades of grass, while their conductivity 
is much greater, so that they receive heat by conduction 
from the ground below, to make up in part for that which 
they lose by radiation. 

On account of the great radiating power but small con¬ 
ductivity of straw, the water in shallow vessels, if exposed 
upon a heap of straw, may be frozen during the night in 
hot regions of India. 

The theory of Dew was first clearly worked out by 
William Charles Wells, a London Physician, and the student 
interested in the subject is recommended to consult his essay, 
edited by Mr L. P. Casella, and published by Messrs Long¬ 
man and Co. in 1866. 

275. When the temperature of the surface of the ground, 
or of other surfaces, is reduced by radiation below 0°C., this 
temperature being also below the dew-point of the surround¬ 
ing air, the aqueous vapour becomes frozen as it is condensed, 
and thus hoar-frost is produced. 

Black-frost is produced when the aqueous vapour, instead 
of subliming into hoar-frost, is first condensed into liquid 
water and then frozen. 

276. It has been stated (Art. 237) that dry air is much 
more diathermanous than air containing aqueous vapour. 
Hence in sandy deserts, where there is^ very little vapour in 
the air, not only is the earth intensely hot during the day, 
but at night, through the unchecked radiation, it becomes 
intensely cold. 


CHAPTER XL 


ON THE CONSERVATION OF ENERGY AND THE CONNECTION 
BETWEEN MOTION AND HEAT. BACON. RUMFORD. DAVY. 
SEGUIN. MAYER. JOULE. SPECIFIC HEAT OF AIR AT 
CONSTANT VOLUME. HEAT ENGINES. DISSIPATION OF 
ENERGY. 


277. Force is said to do work when it moves its point of 
application. 

The work done by a force which remains uniform in 
magnitude and direction, is measured by the product of the 
number of units of force, and the number of units of length 
through which its point of application is moved in the direc¬ 
tion of the force } that is, through which the force works. 

If the weight of 1 lb. be the unit of force, and 1 foot the 
unit of length, the work done by a force equal to the weight 
of 1 lb. in working through 1 foot is the unit of work, and 
is called a foot-pound. 

For example, if a weight of 10 lbs. be allowed to fall from 
a height of 6 feet to the ground, since the earth exerts an 
attractive force upon it in the direction of motion equal to 
the weight of 10 lbs., the work done upon the body by 
gravity is 60 foot-pounds. 

278. Work is said to be done against a force, when the 
point of application is made to move (by some agent) in the 
direction opposite to that in which the force acts, and is 
measured by the product of the number expressing the force 
and that expressing the distance moved over by its point of 

G. 12 


178 


WORK DONE AGAINST GRAVITY. 


application in the direction opposite to that in which the 
force acts. 

Thus, if the 10 lb. weight above mentioned be raised 
from the ground to its original position at a height of 6 feet, 
60 foot-pounds of work are done against gravity. 

The work done in lifting 1 cwt. of bricks to the top of 
a scaffold 40 feet in height will be the same, viz. 4480 
foot-pounds, whether the bricks be raised in a basket over a 
pulley along a vertical straight line through 40 feet, or whether 
they be carried in a hod up an inclined ladder, or wheeled in 
a barrow up planks at a small inclination to the horizon, 
although in this last case the whole distance through which 
they are moved is very much greater than 40 feet. We see 
then, that in order to find the work done against gravity, we 
have simply to multiply the weight of the body in pounds 
by the vertical height through which it is raised in feet, 
and the product is the required number of foot-pounds of 
work, and a similar process will give us the work done by 
gravity on a descending body, the weight of the body and 
the difference of level between its initial and final positions 
being all that concerns us, the form of the path described 
having no influence on the result. 

279. Hence in the case of a force whose direction is con¬ 
stant, if the point of application of the force do not move 
in the same straight line in which the force acts, we must 
determine the whole distance through which it has moved 
parallel to this straight line, and if this be given the work 
done by, or against, the force is independent of the path 
along which the point of application moves. 

280. If a weight of 10 lbs. be suspended at a height of 
6 ft. from the ground by a string passing over a smooth 
pulley it will be able, in descending, to lift a weight less than 
10 lbs., but differing from it by a quantity as small as we 
please, and attached to the other end of the string, through 
the same height; and we may therefore say that in virtue 
of its position relative to the earth, it is capable of doing 
60 foot-pounds of work upon another body, or to speak 
more correctly, the system composed of the 10 lb. weight 


POTENTIAL ENERGY. KINETIC ENERGY. 179 

and the earth, is capable of doing 60 foot-pounds of work 
in virtue of the relative positions of these bodies. Similarly 
if a spring be compressed it is capable of doing work (in 
virtue of its compression) when allowed to resume its natural 
form. 

281. Again, if we succeed in catching a cricket-ball in 
one hand, we are conscious of a pressure exerted by the ball 
on the hand, and we also observe that the ball compels the 
hand to move backwards over a certain distance in the 
direction in which the ball is moving, that is, in the di¬ 
rection in which it presses the hand. Hence the ball does 
an amount of work on the hand, which, if the pressure 
exerted by it were uniform, would be measured by the 
product of this pressure, and the distance through which 
the hand moves in the direction of the pressure. The ball 
is therefore capable of doing work in virtue of its motion. 
If the ball were to fall on the top of a spring it would bend 
the spring by doing work upon it, and would thus put the 
spring in a position to do work on being allowed to regain 
its original form. (It may be shewn that the amount of 
work the ball can do is proportional to the product of its 
mass and the square of its velocity.) 

Of course the cricket-ball is unable to do work unless it 
meets with some object not moving with the same velocity 
as itself, so that, in strictness, we ought to say that the 
system consisting of the ball and the object which it strikes 
is capable of doing work in virtue of the relative motion 
of the parts. When we speak of the work which a moving 
terrestrial body can do, we generally mean the work it 
can do in being brought to rest relatively to the earth. 

282. Hence we see that a system of bodies may be 
capable of doing work in virtue of its configuration, that is 
the relative positions of its parts, or, of its motion. The whole 
amount of work which a system is capable of doing is 
called its energy. That portion of its energy which is due 
to its motion is called its kinetic energy, while that portion 
of the energy which is due to its configuration, is called 
potential energy. 

12—2 


180 


ABSOLUTE UNIT OF FORCE. 


288. Potential energy and Kinetic energy are mutually 
convertible. Thus if a weight of 10 lbs. be held at a height 
of 6 ft. above the ground, it may be said to possess 60 foot¬ 
pounds of potential energy in virtue of its position relative 
to the earth. If it be allowed to fall freely from this height, 
at the instant it reaches the ground its potential energy is 
zero, but it has a considerable velocity, and the kinetic 
energy it possesses in virtue of this motion is exactly equi¬ 
valent to 60 foot-pounds. If the velocity were now reversed 
this kinetic energy would be at first the same as before, 
but the body would now continue to rise, losing velocity 
and therefore kinetic energy as it goes, until it would come 
to rest at a height of 6 ft. from the ground where its kinetic 
energy would be zero, since it would be at rest, but its 
potential energy would be 60 foot-pounds. Of course if it 
remained unsupported it would immediately begin to de¬ 
scend again, and the same cycle of events might be repeated, 
so that we should have the potential energy originally 
possessed by the ball, alternately converted into kinetic 
energy, and this reconverted into potential energy. This 
actually takes place in the case of the motion of a clock 
pendulum, or any vibrating body, the energy of which is 
potential when at the extremity, and kinetic when in the 
middle, of its swing. At any intermediate point the energy 
is partly potential and partly kinetic. The energy of a bent 
spring is potential energy, while that of a cannon-ball after its 
discharge is kinetic energy. 

It is possible that if we knew more about the constitution 
of matter and the machinery by which one particle acts 
on another at a distance we should have no need for this dis¬ 
tinction between Kinetic and Potential energy. At first 
sight the energy of a quantity of compressed air, or of 
the high-pressure steam in a boiler, appears to be like that of 
a compressed steel spring and we should class it as potential 
energy. But the dynamical theory of gases teaches us that 
this energy is due to the motion of the gaseous particles, the 
pressure of a gas being simply due to the impacts of the 
molecules upon any surface exposed to them. Hence we 
must regard the energy of compressed gases as Kinetic 
energy, and perhaps if we knew as much about the nature of 


ABSOLUTE UNIT OF FORCE. 181 

solids and liquids as we think we know about gases we 
might see a reason for regarding all kinds of energy as 
Kinetic energy. 

284. It should be observed that the units of force and of 
work we have adopted, viz. the weight of a pound, and the 
foot-pound, both belong to a class of variable units called 
gravitation units, for a pound is properly a definite quantity 
of matter, and its weight depends upon the locality in which 
it is placed, as well as its height above the sea-level, since 
the intensity of gravity varies both with the latitude and 
the distance from the earth’s centre. On this account these 
units are not well adapted for general use throughout the 
world, and other units, called absolute units, which do not 
depend on the attraction of the earth, have been employed 
to supersede them. 

The British Absolute unit of force is that force which 
acting on a pound of matter for a second, generates, in it 
a velocity of one foot per second, and is called a poundal. The 
British Absolute unit of work is the work done by this force 
in working through one foot, and is called a foot-poundal. 

This unit of force is rather less than the weight of half 
an ounce in the latitude of London. 

The power of an agent is the rate at which it can work. 
The British Absolute unit of power is that of an agent which 
can work at the rate of one foot-poundal per second. 

An agent which can work at the rate of 33,000 foot¬ 
pounds per minute or 550 foot-pounds per second is said to 
be of one Horse-Power. It will be noticed that the Horse- 
Power is a gravitation unit, not an absolute unit, of power. 

The term horse-power is often used in connection with 
the rate at which an engine or other agent is actually work¬ 
ing and without reference to the greatest rate at which it 
can work. 

285. The units of length, mass and time generally em¬ 
ployed in scientific work are the centimetre, gramme and 
second, and units based upon these are frequently distin¬ 
guished by the letters C. G. S. 


182 


CONSERVATION OF ENERGY. 


The C. G. S. unit of force is that force which, acting on a 
gramme for a second , generates in it a velocity of a centimetre 
per second , and is called a Dyne. 

The C. G. S. unit of work is the work done by a Dyne in 
working through a centimetre , and is called an Erg. 

The weight of a Gramme at the sea level in Paris is 
equal to about 981 Dynes. 

Since the erg is an extremely small unit of work, being 
equal to little more than the work done in lifting a milli¬ 
gramme through a centimetre, it is convenient to employ a 
.larger unit for practical purposes. The joule is such a unit 
and is equal to 10,000,000 ergs. 

The G. G. S. unit of power is the power of an agent which 
can work at the rate of an erg per second. 

A rate of working equal to 10,000,000 ergs per second is 
called a watt. 

286. Newton in commenting on the third law of motion 
makes a statement which may be translated as follows:— 

“If the action of an agent be measured by the rate at 
which it works , and the reactions of the resistances , whether 
arising from friction , cohesion , or weight by the rate at 
which work is done against them, and if amongst these re¬ 
actions we include the rate at which kinetic energy is being 
generated in the system , action and reaction in all combi¬ 
nations of machines are equal and opposite .” 

This statement is equivalent to asserting that when 
an agent does work on a system, the whole of the work 
done is equivalent to the work done against gravitation, 
cohesion, friction (and other forces) together with the kinetic 
energy generated in the system. Now we have seen that 
when work is done against gravity, an equivalent amount 
of potential energy is conferred on the body which is raised, 
and the same is true when work is done against any forces 
which, like gravity, are independent of time and of the 
motion of the system. Hence if a system be acted on by 
forces of this nature only, Newton's statement is equivalent 


CONSERVATION OF ENERGY. 


183 


to the assertion that the work done on the system by any 
agent is equivalent to the change produced by it in the sum 
of the potential and kinetic energy of the system. This is 
a case of the great Principle of the Conservation of Energy. 
In particular, we see that if no external agent affect the sys¬ 
tem the sum of its 'potential and kinetic energy will remain 
constant. 

287. If work be done against friction, or force of a like 
nature, no potential energy is conferred on the moving 
system, for friction always acts so as to prevent motion, 
and can therefore have no tendency to bring a body back 
into its original position, as gravity tends to do when a 
weight is raised. 

The work done against friction, therefore, appears at first 
sight to be lost, and for a long while this was believed to be 
the case. It has its equivalent, however, in the energy due 
to a motion which we have not yet considered. 

288. If a brass button be rubbed vigorously on a board 
and then applied to the skin, we become conscious that the 
button is hot. The physical agent which produces this sensa¬ 
tion is called heat (Art. 1). Now the work done upon the 
button by the person rubbing it is not in this case converted 
into energy of position, as the button may be finally brought 
to rest at the point from which it started, nor is any portion 
of it finally converted into the energy of motion of the button 
as a whole, since it is at last brought to rest. It remains then 
for us to discover what has become of the work done on the 
button. 

289. If a resined bow be rubbed against the string of a 
violin, both friction and adhesion tend to retard the motion, 
and work has to be done against these forces by the hand of 
the violinist. After the passage of the bow the instrument 
emits a musical note, and on examination it is found that the 
string is in a state of vibration , a state which it also com¬ 
municates to the wood of the violin, whence most of the 
sound is emitted. In this case the work done by the hand 
of the violinist is partly transformed into the energy of the 
vibrating string and sound-board, and thence into the energy 
of sound-waves in air. 


184 HEAT PRODUCED BY FRICTION. 

Again, if a number of elastic wires have each one end 
stuck into a board, like bristles in a brush, and the hand 
be made to pass over their tops, the work done by the hand 
will produce vibrations in the wires which will be in part 
communicated to the board. The surface of any body which 
is not perfectly smooth, a condition fulfilled by no known 
object, consists of a series of small projections, and the 
passage of a rough surface over these causes them to vibrate, 
in the same manner as vibrations are set up by the passage 
of the hand over the wire brush, or of the bow over the violin¬ 
string, though, of course, on a very much smaller scale. Now 
it is the passage of these projections on each surface, over 
one another, that is the cause of friction, and the work 
done against friction is consumed in setting up vibrations in 
these small portions of matter, these vibrations being con¬ 
tinually communicated to the other material particles in 
contact with them, (conduction of heat,) so that vibrations 
are set up in every particle of which the button or other body 
is composed. (All natural surfaces possess projections of this 
nature; the art of polishing consists in making them as small 
as possible. A surface is highly polished when they are small 
compared with the length of a wave of light, or the 50,000th 
of an inch.) It is this state of vibration which when com¬ 
municated to our nerves produces the sensation of heat, and 
the whole of the work done against friction is converted into 
the energy of vibration of the particles of which the bodies 
which rub against each other are composed. (The part 
played by local electric currents as an intermediate form 
assumed by the energy in this production of heat has not 
been determined.) 

290. We can now place the conservation of energy upon 
a broader basis than before, comprehending within it those 
cases in which work is done against friction and similar non¬ 
conservative forces, and may enunciate it thus :— 

When an Agent does work on any material system , the 
whole of the work done is equivalent to the change of the 
sum of the 'potential and kinetic energy of the system , in¬ 
cluding in the latter the energy of the vibrations set up in the 
molecules of which the system is composed . If the system do 


BACON ON THE NATURE OF HEAT. 


185 


work against an external resistance its loss of energy is equi¬ 
valent to the work so done. 

We thus see that the work done against friction and 
supposed by Newton to be lost, has its equivalent in mole¬ 
cular vibrations, constituting heat, generated in the system. 

Maxwell stated the Principle of the Conservation of 
Energy very elegantly as follows : 

“ The energy of a system is a quantity which can neither be 
increased nor diminished by any actions between the parts of 
the system though it may be transformed into any of the forms 
of which energy is susceptible.” 

291. In the case of the vibrating violin-string, the 
vibrations are communicated by the sound-board of the 
instrument, and, in small part, by the string itself, to the 
surrounding air, through which they are propagated to dis¬ 
tant objects, and their energy is lost by the violin. In a 
similar way the vibrations which, as we have said, constitute 
heat in bodies, are slowly imparted to a medium which fills 
space, viz. the ether, and are propagated by it to distant 
bodies in the form of radiant energy, which may or may not 
be capable of producing the sensation of light, and energy is 
then lost by the body in which it originally existed as heat. 
It is the communication of vibrations from particle to par¬ 
ticle of a body which constitutes the conduction of heat. 

292. It was formerly believed that heat consisted of 
a kind of imponderable fluid which pervaded all bodies, 
and that when heat was produced by the blow of a ham¬ 
mer, or the sudden compression of air, it was squeezed out 
of the body operated upon, by the pressure to which it was 
exposed. 

Long before the Dynamical Theory of heat was esta¬ 
blished, Lord Bacon expressed his conviction that heat 
consists of a kind of motion or “ brisk agitation ” of the 
particles of matter. In the Novum Organum, after giving 
a long list of sources of heat, in which he mentions the 
friction of trees rubbing against one another in a high wind, 
and other mechanical sources, he says: “From these exam¬ 
ples, taken collectively as well as singly, the nature whose 


186 


COUNT RUMFORD. 


limit is heat appears to be motion” Again, “It must not be 
thought that heat generates motion or motion heat, though 
in some respects this is true, but the very essence of heat , or 
the substantial self of heat , is motion and nothing else.” But 
Bacon was too apt to theorise without sufficient experi¬ 
mental evidence, and the following quotation almost spoiled 
what he had previously said: “ Comparing the effects of 
fire with those of time ; time dries, consumes, undermines, 
and reduces to ashes as well as fire, and perhaps to a much 
finer degree; but as its motion is very slow and attacks 
very minute particles, no heat is perceived.” He also con¬ 
fused the acrid and irritant properties of acids, essential 
oils, and the like, with heat, and though he cites many 
observations which afford very strong evidence in favour 
of the Dynamical Theory of heat, yet we must give to 
Rumford and Davy the credit of having established it on 
a scientific basis. 

293. Benjamin Thompson, Count Rumford, was en¬ 
gaged by the Bavarian government at the military arsenal 
in Munich. While superintending the boring of cannon he was 
struck by the amount of heat produced by the action of the 
boring-bar on the gun-metal castings, and this induced him 
to determine, if possible, whether or not there existed an 
igneous fluid or caloric to which the sensation of heat was 
due. To account for the heat developed by the boring-bar, 
the first source which presented itself, as that from which 
the heat might have been derived, was the metal abraded 
by the borer. If this were the case, he argued, the capacity 
for heat of the chips ought to differ from that of the solid 
metal by an amount sufficient to account for the whole of 
the heat generated. To ascertain whether this were the case 
he took equal quantities, viz. 1016J grains, of the borings 
and of thin slips cut from the same block of metal with 
a fine saw. The slips of metal were first heated to 210° F. 
and then plunged into water at a temperature of 59J°F., 
contained in a cylindrical tin vessel. After one minute the 
temperature of the water was 63° F. The tin vessel and 
water within it had together the same capacity for heat 
as 4590 grains of water. From these data it will be seen 
that the specific heat of the metal was about Tl. The same 


BUMFOllD’s experiments. 


187 


experiment was then tried with the metallic chips and 
the same result obtained; moreover, each experiment was 
repeated three times with nearly the same results. From 
this Rumford concludes, “ that the heat produced could not 
possibly have been furnished at the expense of the latent 
heat of the metallic chips.” 

291. Rumford next turned up a hollow cylinder which 
was cast in one piece with a brass six-pounder, and sepa¬ 
rated from it by a narrow neck of metal. The weight of 
this cylinder, exclusive of the neck and the rest of the 
casting, was 113T3 lbs. A blunt steel borer exerted a 
pressure against the bottom of the cylinder equal to the 
weight of about 10,000 lbs. After the cylinder had made 
21 revolutions per minute for 30 minutes, its mean tem¬ 
perature was found to be 130° F., while its temperature 
before the operation was 60° F. The borings detached from 
the metal during the process amounted to only 837 grains. 

295. It then occurred to Rumford that this heat might 
possibly be due to the action of the air, and in order to 
test this he surrounded the small cylinder by a wooden 
box, through one side of which the square boring-bar passed, 
while the narrow neck which connected the cylinder with the 
cannon fitted a circular hole in the opposite side of the box, 
in which it could turn freely. About 18*77 lbs. of water 
were placed in the box so as to completely cover the cylinder, 
and the brass casting was made to turn at the rate of 
32 revolutions per minute by the action of two horses, 
though Rumford remarks that one horse would have been 
sufficient for the work. The temperature of the water at 
the commencement of the experiment was 60° F.; in 2J 
hours it boiled. Taking into account the heat required 
to raise the temperature of the gun-metal cylinder and 
of that part of the boring-bar which was within the water, 
Rumford estimated that the heat produced was sufficient 
to raise 26 58 lbs. of water from the freezing-point to the 
boiling-point, and this calculation neglects the heat ab¬ 
sorbed by the box and that dissipated by conduction and 
radiation. The quantity of metal borings produced during 
the experiment amounted to 4145 grains. From this result 
Rumford concluded that the work of one horse was capable 


188 RUMFORD. DAVY; 

of generating heat more rapidly than nine ordinary wax 
candles burning in the usual manner. 

296. Finally Rumford reviewed the sources from which 
the heat might, a priori, have been thought to have been 
derived. That it could not have come from the borings was 
shewn by the first experiment. It could not have been due 
to the action of the air, for it was produced just as readily 
when the whole apparatus was filled and surrounded with 
water. It could not .have come from the water, for this 
received heat, and no chemical or other change took place 
in the water itself to account for the heat generated. That 
the heat should have come from the boring-bar or neck of 
metal connecting the cylinder with the gun, appeared more 
improbable than the previous hypotheses, for throughout the 
experiment heat was escaping from the apparatus by each 
of these channels. Moreover, “ the source of the heat gene¬ 
rated by friction in these experiments, appeared evidently to 
be inexhaustible.” 

“ It is hardly necessary to add, that anything which any 
insulated body, or system of bodies, can continue to furnish 
without limitation, cannot possibly be a material substance; 
and it appears to me to be extremely difficult, if not quite 
impossible, to form any distinct idea of anything capable of 
being excited and communicated in the manner the heat 
was excited and communicated in these experiments, except 
it be Motion.” (Rumford.) 

297. About the same time as Rumford s experiments 
were published (1798), Sir Humphry Davy shewed that if 
two pieces of ice were made to rub against one another, 
even in a vacuum, though everything surrounding them 
were at a temperature below the freezing point, the pieces of 
ice could be melted by the friction. In this case the heat 
could not have come from the ice, for heat is absorbed by it 
in fusing. Davy did not, however, see at the time that 
this experiment afforded conclusive evidence against the 
theory of the material nature of heat. 

298. The experiments of Rumford and Davy shewed 
that an unlimited amount of heat could be obtained by 


MECHANICAL EQUIVALENT OF HEAT. SEGUIN. 189 


purely mechanical means, and completely disproved the 
material or caloric theory of heat. The researches of Joule 
shewed that when heat is produced by mechanical means, 
no matter how complicated the mechanism may be, or what 
transformations of energy take place, the quantity of heat 
produced is always 'proportional to the quantity of energy 
expended in producing it, or the production of one unit of 
heat always requires the performance of the same number of 
units of work. Since for each unit of heat produced, the 
same quantity of energy, in some form or other, disappears, 
no matter how the process may be conducted, it follows that 
energy is the mechanical quantity which corresponds to heat, 
the other forms of energy being actually converted into heat. 
Thus heat is only one of the many forms of which energy is 
susceptible. 

299. Def. The quantity of energy which , if entirely 
converted into heat, is capable of raising the temperature of 
the unit mass of water from 0° C. to 1° G. is called the mecha¬ 
nical equivalent of heat 

Seguin, a nephew of Montgolfier, was one of the first to 
attempt to measure the mechanical equivalent of heat. He 
argued that, if heat be energy, when a steam-engine does 
work, some of the heat of the steam must be consumed, and, 
consequently, less heat will leave the engine than if the 
same quantity of steam were blown through without doing 
any work. Hirn, in 1857, succeeded in detecting this differ¬ 
ence experimentally, and also in measuring it. From his 
result, knowing the amount of w r ork done by the engine, 
he calculated approximately the mechanical equivalent of 
heat. 

300. Seguin, in 1837, endeavoured to determine the 
mechanical equivalent of heat from the loss of heat suffered 
by steam in expanding, but he assumed that the whole of 
this heat was consumed in doing work against the pressure 
to which the steam was exposed, taking no account of the 
change in the condition of the steam itself. 

301. In 1842, Mayer, a physician at Heilbronn, published 
an attempt to determine the mechanical equivalent of heat 
from the heat generated in the compression of air, but he 


190 MECHANICAL EQUIVALENT OF HEAT. MAYER. 


made the same assumption as Seguin. Joule subsequently 
shewed that when air is compressed nearly the w T hole of the 
work done is converted into heat, but this Mayer had no 
right to assume without experimental evidence. On account 
of errors in his values of the specific heats of air at constant 
pressure and at constant volume, Mayer’s result was con¬ 
siderably in error. 

The omission made by Mayer and Seguin in their reasoning 
on this subject may be illustrated by taking a somewhat 
extreme example. Suppose energy expended in compressing 
a helical steel spring; a certain amount of heat will be 
generated on account of the imperfect elasticity of the steel 
but this will absorb but a very small fraction of the energy 
expended in compressing the spring. The rest of the energy 
will be expended in changing the relative positions of the 
particles of steel in opposition to the forces which act between 
them. When the spring returns to its natural form this energy 
is again liberated and may be employed in doing an amount 
of work nearly equal to that done in compressing the spring. 
If in the case of air or steam there were forces acting between 
the particles tending to keep them in some definite position 
relative to one another and to oppose any change of position, 
it would follow that on compressing the material more or 
less of the work done would be expended in doing work 
against the molecular forces, and would be stored as potential 
energy in the compressed substance to be liberated in doing 
external work when the pressure is relieved. The amount of 
heat (kinetic energy) produced by the compression would 
consequently be less than the equivalent of the work done in 
compression by the amount of potential energy so accumulated. 
When Joule shewed that no potential energy was liberated 
when air expanded into vacuum (Art. 308) he also proved 
that no forces were exerted between the particles of air at 
their ordinary distances apart. 

302. To Dr Joule, of Manchester, belongs the credit of 
having first determined the mechanical equivalent of heat 
with great accuracy by a course of investigation which was 
logically complete. His best experiments were carried out 
in 1849, and consisted in determining the amount of heat 
generated by the friction of a metal paddle in vessels con- 


MECHANICAL EQUIVALENT OF HEAT. JOULE. 191 

taming water and mercury, and also by the friction of bevel 
wheels of cast iron against each other, the amount of work 
expended in driving the apparatus being measured. The ar¬ 
rangement employed to produce friction in water consisted of 
eight paddles made to revolve in a cylin¬ 
drical box of water between stationary 
vanes, as in an ordinary churn. The forms 
of the paddles and vanes are shewn in fig. 

51. The paddles were made to revolve by 
a weight which in its descent turned a 
roller, around which part of a string was 
wound, another part of the same string 
being wound round the cylinder A, which 
could be coupled, by a pin B, to the pad¬ 
dle. When the weight had run down 
it was wound up by turning the handle 
H after removing the pin B , when, the 
coupling being removed, the paddle was 
unaffected by the motion of the handle. 

The mass of the driving weight being 
known, as well as the whole distance 
through which it fell, the whole amount of work done upon 
the apparatus was determined in foot-pounds, and allowance 
made for all resistances outside the box containing the water, 
and for the small amount of kinetic energy possessed by 
the weights when they struck the ground. The temperature 
of the water in the vessel was observed during the experi¬ 
ment, and thermometers which could be read to ^r°F. were 

employed; the amount of water as well as the capacity for 
heat of the vessel and paddle were carefully measured and 
allowance made for conduction. These experimental data are 
all that are required for the determination of the mechanical 
equivalent of heat, and the results shewed that the amount 
of work which must he entirely converted into heat, in order 
to raise the temperature of one pound of water 1° G. from 0° C., 
is 1390*846 foot-pounds. 

303. The apparatus employed by Joule for stirring 
mercury was similar to that described in the last article, but 
somewhat smaller and made of iron. In another set of 















192 


MECHANICAL EQUIVALENT OF HEAT. 


experiments he employed cast iron wheels, bevelled so as to 
form portions of a hollow and of a solid cone, and these were 
made to grind against one another, the solid cone being 
pressed into the other by means of a lever, and the rotation 
kept up by a falling weight. Two sets of weights were 
employed in different experiments, the larger pair being 
about 58 lbs. and the smaller 19 J lbs. 

304. The extreme results of all these experiments 
varied by little more than one-half per cent., although the 
experiments differed so widely in their details, and from 
them Joule inferred that “the amount of heat produced 
by friction is proportional to the work done and inde¬ 
pendent of the rubbing surfaces,” and that the mechanical 
equivalent of heat is about 1390 foot-pounds. 

Hence, according to Joule, 

If the amount of heat required to raise a pound of water 
from 0° G. to 1° C. he taken as the unit of heat, the mechanical 
equivalent of heat is 1390 foot-pounds. 

This is usually denoted by J. 

If a quantity of water fall freely through 1390 feet, the 
heat produced in bringing it to rest would raise the tempe¬ 
rature of the water through 1°C. 

305. The experiments just cited afford the most satis¬ 
factory determinations of the mechanical equivalent of heat, 
but were not the first of Joule’s experiments on the subject. 
In 1840 Joule shewed that if a magneto-electric machine 
were employed to produce an electric current, and the energy 
of the current entirely converted into heat in the conductors 
through which it passed, the amount of heat so produced was 
the same as if the energy employed in driving the machine 
had been directly converted into heat by friction or other 
mechanical means, without the intervention of the current. 
He also shewed that the whole heat generated in a voltaic 
circuit was proportional to the work done by the electro¬ 
motive force of the battery. 

306. Knowing the mechanical equivalent of heat, we 
can determine the amount of heat generated in any mecha¬ 
nical action if we know the number of foot-pounds of energy 
transformed. 


MECHANICAL EQUIVALENT OF HEAT. 


193 


For example, the amount of heat which would be pro¬ 
duced by the fall of 100 tons of stone through a vertical 
height of 1000 feet down the side of a mountain, supposing 
the mass to come to rest at the end of this distance, would raise 

,, , . , 2240 x 100 x 1000 , 

the temperature of -T‘ v 90-pounds, — 161,151 

pounds, of ice-cold water 1°C., or would convert about 253 
lbs. of water initially at 0°G. into steam at 100° C. 

(In this case, as explained above, the potential energy 
initially possessed by the earth and stone on account of 
their relative positions is converted into kinetic energy in 
the fall and this into heat, or thermic energ}', by striking 
the ground.) 

307. We have seen that work may be readily converted 
entirely into heat. Heat must therefore be of the same 
nature as work, that is, a form of energy, and by means of 
its mechanical equivalent quantities of heat and of ether 
forms of energy become comparable. 

As work can be converted into heat, so, by proper appli¬ 
ances, heat may be converted into work. An appliance for 
this purpose is called a heat engine. Steam engines, hot air 
engines, gas engines and the like, are forms of heat engines. 
The conversion of heat into work may be shewn by taking a 
quantity of air compressed in a tall cylinder by a number of 
weights placed upon a piston which fits it. By removing the 
weights one by one the air will expand, and in doing so will 
lift the weights left on the piston, and therefore do work. If 
the weights be removed in sufficiently quick succession the 
air will be found to be cooled by its expansion. Now Joule 
shewed that when air expanded into vacuum, and consequently 
did no external work during its expansion, its temperature 
was on the whole unaffected. Hence the fall of temperature 
of the air lifting the weight must be due to a conversion of 
part of its heat into work*. Again, it is found that more 

* The molecular theory of gases completely explains this result, because, 
when the piston is rising it is moving in the direction in which the particles 
of gas strike it; they therefore rebound with diminished velocity, and al¬ 
though they behave like perfectly elastic balls, they lose energy, that is, 
they lose heat, by the impact. 

a. 


13 



194 


CONVERSION OF HEAT INTO WORK. 


heat is required to raise the temperature of a mass of air 
through a given number of degrees when it is allowed to 
expand against a constant pressure than when its volume is 
kept constant, in other words, the specific heat of air at con¬ 
stant pressure is greater than its specific heat at constant 
volume. Brft its temperature is unaffected by change of 
volume when it does no external work though no heat is s 
allowed to enter or leave it. Hence the difference between 
the two specific heats must be due to the heat converted into 
external work when the gas is allowed to expand. 

308. The experiment by which Joule shewed that the 
whole of the heat absorbed by a gas expanding at constant 
pressure was consumed in doing external work, was under¬ 
taken in order to justify one of his modes of determining 
the mechanical equivalent of heat. Air at a pressure of 22 
atmospheres was allowed to escape from a vessel through 
a coil of very fine lead tube, and finally to escape into the 
air. The vessel containing the compressed air was placed in 
a calorimeter, as was also the tube, and the heat produced 
by the escape of the air measured. The energy required to 
compress the air in the vessel could be easily calculated, and 
to complete the determination it was only necessary to know 
that no heat is consumed by air in expanding at constant 
temperature when it does no work. To test this, Joule 
connected together two equal vessels, one containing air at 
a pressure of 22 atmospheres and the other exhausted. The 
vessels were placed in a calorimeter, and on opening the 
communication between the two, so as to allow the air to ex¬ 
pand, no change took place in the temperature of the water. 
When the two vessels were placed in separate calorimeters, 
the water in that containing the compressed air vessel 
became cooled, while that in the other became heated to 
the same extent. 

309. From what we have said, it will appear that the 
mechanical equivalent of heat enables us, if we know the 
specific heat of air at constant pressure, to determine its 
specific heat at constant volume. The method will be made 
clear by the following example. 


SPECIFIC HEAT OF AIR AT CONSTANT VOLUME. 195 


Suppose a cubic foot of air under a pressure of 15 lbs. 
weight per square inch and at 10° C. to weigh ljozs., and 
suppose its specific heat at constant pressure to be *237. 
Let the air be placed in a cylinder closed by a piston whose 
area is one square foot, the weight of the piston being so 
counterpoised that the pressure on the air in the cylinder 
is equal to the weight of 15 lbs. on each square inch. Then 
the whole pressure of the air on the piston will be equal 
to the weight of 144x15 lbs., that is, of 2160 lbs. Now 
let the air be heated to 100° C. It will then expand (Art. 107) 
373 

till its volume is —cubic feet, and will therefore raise the 
Zoo 


Hence the work done by the 


90 

piston through —— feet. 

air in expanding will be — foot-pounds, or about 

687 foot-pounds. The mechanical equivalent of heat being 
1390 foot-pounds, the amount of heat consumed in doing this 

work would raise the temperature of P oun( ^ s 

water 1° C. 

5 

Now the mass of air heated is 1J oz. or ^ of a pound, 

and its temperature is raised through 90° C., its specific 
heat being *237. The amount of heat employed would there- 

„ 5 x 90 x *237 „ 

fore raise through 1° C. the temperature of-^ ids. 

of water, or of 1*666 lbs. of water. But of this number of 

units of heat 1390 ’ ° r un ^ s * s consume d * n doing 

external work. Therefore the amount employed in actually 
raising the temperature of ^ lbs. of air through 90° C. is 

1*6666 - *4942, or 1*1724 units. But since air is not cooled 
by expansion if it do no external work, this amount is the 
same as would be required to raise the temperature of the 
same air to the same extent, if its volume were kept constant. 

Hence to raise the temperature of gjlbs. of air through 90° C. 

13—2 






196 


HEAT ENGINES. 


at constant volume we require 1*1724 units of heat, and the 
specific heat of air at constant volume is therefore 

90 x 5 

From this we see that the ratio of the specific heat of 
air at constant pressure to its specific heat at constant 
*237 

volume is =1*42... According to the best experi- 

*166... 

ments the value of this ratio for air and other permanent 
gases is between 1*41 and 1*42. 

310. We have said that heat engines are capable of 
converting heat into work, and this is usually effected by 
taking advantage of the expansion of some substance w r hen 
heated. This substance is called the working substance. 
If the engine, after a complete stroke, leaves the working 
substance in the same state in which it finds it, so that 
it is capable of employing the same substance an indefinite 
number of times in succession, the substance is said to go 
through a complete cycle of changes; as, for instance, when 
the waste steam from an engine is condensed and returned 
to the boiler. 

311. An engine can convert heat into work only by 
allowing heat to pass into the working substance from a 
source at a high temperature, and allowing part of this 
to escape from the substance to a condenser at a lower 
temperature. Thus the engine cannot convert the whole 
of the heat it receives from the source into work. 

The ratio of the amount of heat which an engine converts 
into work to the amount received from the source is called the 
efficiency of the engine. 

In measuring the efficiency of an engine the working 
substance is supposed to be left by the engine in the same 
condition as to temperature and volume as that in which it 
was found by it. Otherwise the engine might utilize some 
of the energy contained in the substance itself , and so leave it 
deprived of part of its energy, as when air does work in 
expanding under a continually diminishing pressure without 
receiving any heat from without. 




EFFICIENCY OF HEAT ENGINES. 


197 


312. If two bodies at different temperatures be placed 
in contact, heat will pass from the hot to the cold body 
without doing any work on the way. We might thus allow 
the whole of the heat from the source to pass into the 
condenser without doing any work. In order then to make 
the most of the heat supplied by the source, we must so 
arrange matters that when heat passes from the source into 
the working substance, or from the working substance to 
the condenser, the difference of temperature in each case 
is the least possible. The efficiency of the engine will then 
be a maximum. 

313. It can be shewn that if this difference of tern* 
perature could be made indefinitely small, and no heat be 
allowed to leave the working substance by radiation or 
conduction, except that which enters the condenser, the 
efficiency of the engine would be very nearly proportional 
to the difference between the temperatures of the source 
and condenser divided by the temperature of the source, 
reckoned from the absolute zero of the air thermometer. 
A scale of temperature for which this proportionality is 
exact instead of approximate is known as Thomsons Abso¬ 
lute scale of temperature, having been first proposed by 
Sir William Thomson. The difference between it and the 
scale of the air thermometer described in Art. 126 is almost 
insensible. This scale is independent of the properties of 
any particular substance, and is therefore entitled to be 
called the absolute scale of temperature. An engine which 
fulfils the above condition is said to be reversible because by 
an indefinitely small change in the temperature of the 
working substance the flow of heat and every action of the 
engine can be reversed, provided that an amount of energy 
be expended by an external agent which is exactly equivalent 
to the work done by the engine when working forwards for 
the same number of strokes. 

314. Suppose an engine which satisfies the above con¬ 
ditions to be supplied by heat from a source at 250° G. and to 
give out heat to a condenser at 100° G. Suppose also that 
the engine works at the rate of 10 horse-power; it is required 
to find the amount of heat taken from the source and the 
amount given out to the condenser per hour. 


198 


AVAILABILITY OF HEAT FOR WORK. 


The measure of the efficiency of the engine h 


250-100 
250 + 273 


or 


150 

523* 


Now the work done per hour is 33000 x 10 x 60 
foot-pounds = 19,800,000 foot-pounds, and this implies the 
conversion into work of —, or 14244 6..units of heat. 
150 

But only of the heat received is converted into work, 

373 
523 

condenser. Hence the number of units of heat received per 

523 

hour from the source is 14244*6 x -=-^= 49666*1..., and the 

ioU 

amount given out to the condenser is this quantity less that 
converted into work, viz. 35421*5... units. 


while the remaining of the heat is given out to the 


315. From what we have said it will appear that our 
ability to convert heat into work depends on our power 
of commanding differences of temperature, and the avail¬ 
ability of any quantity of heat for useful purposes depends 
upon the difference between the temperature of the body 
containing it and the lowest temperature we can command. 
Now if we have a hot and cold body and a heat engine, 
part of the heat of the hot body can be converted into, or 
is available for, work ; but if the bodies be placed in contact 
they will eventually attain the same temperature, and though 
no heat has been lost by the two together, yet that which 
they contain is no longer available for conversion into work 
without the introduction of a colder body. If we could 
obtain no differences of temperature heat engines would 
have no existence. Thus although the whole amount of 
energy possessed by a system of bodies unacted upon by 
anything from without remains unaltered, yet the avail¬ 
ability for doing external work of this energy is continually 
diminishing. The principle involved in this statement is 
called the principle of the Dissipation of Energy. 

316. The following example is interesting since it fairly 
represents the working of some of our best condensing 
engines. 




EFFICIENCY OF STEAM-ENGINES. 


199 


An engine consumes If lbs. of coal per indicated horse¬ 
power per hour. The heat developed by the combustion of 
1 lb, of coal is capable of converting 15 lbs. of water at 100° G. 
into steam at the same temperature. Find what fraction of 
the whole heat generated is employed in doing work in the 
engine. 

To evaporate 15 lbs. of water requires 15 x 537 or 8055 
units of heat. Hence If lbs. of coal develope by combustion 
14096J units of beat, and this amount is equivalent to 
14096 1 x 1390 or 19590187J foot-pounds of energy. 

But one horse-power sustained for one hour means 
343000 x 60 or 1,980,000 foot-pounds of work. The ratio of 
the work done to the mechanical equivalent of the heat 
developed, that is the efficiency of the engine, is, therefore, 
1980000 ,. 1A1 

19590187^ perCent 

317. If the temperature in the boiler be 150° C. and that 
in the condenser 30° C. we may compare the efficiency of the 
engine with that of a perfect engine working between the 
same limits of temperature, thus:— 

The efficiency of the perfect engine will be denoted by 

120 40 ... 

- or -—-. The efficiency of the engine in question is 

423 141 

141 

about T01. The ratio is therefore T01 x — = *375 nearly. 

This shews that considerable improvement may yet be 
effected in the efficiency of steam-engines before we reach the 
theoretical limit corresponding to the temperature of our 
boilers. 

318. From what has been said it appears that the 
efficiency of an engine may be expected to improve if the 
difference of temperature between the boiler and the con¬ 
denser can be increased, and that for the same difference of 
temperature the efficiency will be greater the lower the 
temperature of the boiler. Hence condensing engines are 
more efficient than high-pressure engines in which the steam 
blows off into the air at a temperature above 100° C. 



200 


NEWCOMEN AND WATT. 


With a condensing engine it is not easy to keep the 
temperature of the condenser below about 30° C. Hence to 
keep the difference as great as possible we must raise the 
temperature of the boiler. The diminution of the tensile 
strength of the boiler plates at high temperatures and the 
injury inflicted on the cylinder, lubricants and packing by 
steam at very high temperature, however, assigns a pretty 
definite limit to the boiler temperature, and it is very seldom 
indeed that a temperature of 200° C. is permitted. 

319. In Newcomen's pumping engine steam was 
employed beneath the piston simply to raise the piston 
against the pressure of the atmosphere and at the same time 
the weight of the pump rods suspended from the other end of 
beam forced up the water from the mine or well as the rods 
descended. Cold water was then injected into the cylinder 
condensing the steam and the atmospheric pressure forced 
down the piston, raising the pump rods in readiness for 
another stroke. But the cold water in the cylinder cooled 
the metal and a large quantity of steam had to be blown into 
the cylinder to raise its temperature again to 100° C. before 
the piston could be lifted for the next stroke. This entailed 
a great waste of heat. James Watt’s greatest invention con¬ 
sisted in the application of the separate condenser, which is 
a chamber kept cool either by the application of cold water 
to its exterior (as in surface condensers) or by the injection 
of cold water into the chamber, or by both these methods. 
When the exhaust port is opened the steam in the cylinder 
has free access to the condenser and in accordance with the 
principle explained in the chapter on Evaporation the pressure 
of the steam in the cylinder must fall to that due to the 
temperature of the coldest part of the enclosure to which the 
steam has access. The separate condenser is therefore as 
efficient in condensing the steam of the cylinder as though 
the condensing water were injected into the cylinder itself 
while the high temperature of the cylinder is maintained. 

320. It is usual to cut off the supply of steam from the 
boiler long before the stroke of the engine has been completed 
and then to allow the steam imprisoned in the cylinder to 
expand and thus drive the piston through the rest of its 


EXPANSIVE WORKING. 


201 


stroke. In a high-pressure engine, which exhausts only into 
the air, it would be useless to allow the expansion to continue 
until the pressure is less than atmospheric pressure, since it 
must be raised to atmospheric pressure when the exhaust 
port is opened; but in condensing engines the steam may be 
allowed to expand until the pressure is very little more than 
that due to the temperature of the condenser, and in some 
classes of engines (pumping engines for example) it is not 
unusual to allow the steam to expand from a total pressure 
of, say, 60 lbs. on the square inch to a pressure of only 3 or 
4* lbs. The temperature of the cylinder being kept con¬ 
siderably above 100° C. while its interior is in communication 
with the condenser (at, say, 30° C.) for half the time during 
which the engine is working it follows that any water which 
finds its way into the cylinder will immediately distil over 
into the condenser, and the interior of the cylinder will 
remain practically dry. Hence, when the steam in the 
cylinder is allowed to expand no evaporation takes place so 
as to provide more steam to keep up the pressure, and the 
pressure falls very nearly in accordance with Boyle’s law. 

321. If a quantity of saturated vapour be compressed 
and no heat be allowed to escape from it its temperature will 
be raised by the heat generated by the compression and at 
the same time its pressure will be increased. It may happen 
that the increase of temperature more than compensates for 
the diminished volume and increased pressure, in which case 
the vapour will remain dry and will in fact cease to be 
saturated (becoming superheated). On the other hand it 
may happen that the increase of temperature does not com¬ 
pensate for the increased pressure, and in this case partial 
condensation will take place. The latter alternative is the 
case with alcohol vapour, but if steam be suddenly compressed 
so that no heat escapes the consequent rise of temperature 
more than compensates for the increase of pressure and the 
steam becomes superheated. In order therefore to keep the 
steam saturated, as its pressure is increased and volume 
diminished, it is necessary to abstract heat from the steam. 
Hence, if a quantity of saturated steam has its temperature 
raised and, at the same time, its pressure increased and 
volume diminished so that it remains saturated, heat must 


202 


SPECIFIC HEAT OF SATURATED STEAM. 


be abstracted from it. In other words, that the steam may 
remain saturated increase of temperature must be accom¬ 
panied by loss of heat. Similarly, decrease of temperature, 
involving expansion and diminution of pressure, will necessi¬ 
tate the communication of heat to the steam if partial con¬ 
densation is to be prevented. These results are sometimes 
expressed by the somewhat curious statement that the specific 
heat of saturated steam is negative . This phrase, of course, 
simply implies that during compression the work done on 
saturated steam raises the temperature more than is con¬ 
sistent with saturation, and to preserve the steam saturated 
heat must be abstracted, while the reverse is, of course, the 
case during expansion. 

322. If saturated steam be allowed to expand, doing the 
full amount of work of which it is capable during the expan¬ 
sion, it loses so much heat that notwithstanding its increased 
volume partial condensation takes place. When this happens 
in the steam ways or cylinder of an engine the condensed 
water accumulates, forming “priming,” and hence in an 
engine working expansively priming is sure to occur and 
some of the steam pressure to be lost unless means are taken 
to prevent condensation. One method consists in surround¬ 
ing the cylinder with a steam jacket, which keeps up the 
temperature of the contents of the cylinder by heat conducted 
through the sides of the cylinder. The principal difficulty 
consists in causing the steam to take up the heat with 
sufficient rapidity. 

323. The more common plan however is to employ 
steam which is not saturated when it enters the cylinder, 
but superheated. The steam in the boiler being in the 
presence of water is of course saturated but on leaving the 
boiler it is made to pass through heated pipes whereby its 
temperature is raised, without, of course, affecting its pres¬ 
sure, and the steam becomes superheated. The steam thus 
superheated can afford to lose a certain amount of heat 
without condensing, and if sufficient heat has been communi¬ 
cated to it, it may be capable of expanding to many times its 
volume, doing work all the while, and still remain dry steam. 
In engines of the locomotive type this superheating is gene¬ 
rally effected by causing the steam on leaving the cylinder to 


SUPERHEATED STEAM. 


203 


pass through tubes placed in the smoke box of the engine 
and exposed to the action of the products of combustion as 
soon as they have passed through the boiler tubes. In order 
that the steam may be as dry as possible when it leaves the 
boiler the steam pipe collects the steam from a steam chest 
placed above the general level of the crown of the boiler. 

In starting a locomotive the valves are generally so 
arranged that for the first few strokes the cylinder is filled 
with steam at full boiler pressure. This serves the double 
purpose of raising the temperature of the cylinder as quickly 
as possible and also of keeping up the pressure on the piston 
just when the greatest pressure is required, viz. in starting 
the train. 


CHAPTER XII. 


ON INDICATOR DIAGRAMS. 

324 . If we draw two straight lines Ov and Op at right 
angles to one another and agree that distances measured from 

Fig. 52. 

V 

M _ P 


O 1 Y V 

0 along Ov shall represent volumes while distances measured 
along Op represent pressures, then any point, P, may be 
regarded as representing the condition of a substance, as far 
as its volume and pressure are concerned; for drawing PN 
and PM perpendicular to Ov and Op respectively, ON or 
MP may be taken as representing the volume of the 
substance and OM or NP its pressure. 

325. If the volume and pressure of the substance under¬ 
go any variation, but are always represented by the point P, 






ISOTHERMAL LINES. 


205 


it is clear that P must change its position, and since the 
condition of a substance cannot change except by a steady 
increase or decrease (although this may take place very 
rapidly) it follows that if the point P always represent both 
the volume and pressure P must move along some definite 
line, generally curved, and this line will, by its form, represent 
graphically the law connecting the variations in volume and 
pressure which the substance undergoes. Such a line is 
called an indicator diagram. 

326. For example, suppose the substance to be a gas 
which is kept at constant temperature and strictly obeys 
Boyle’s law. Then if the pressure be doubled the volume 
will be reduced to one half, and if the volume be doubled the 
pressure will be correspondingly reduced, the product of the 
volume and pressure remaining always constant. Hence P 
will move so that the rectangle PM ON is of constant area. 
(This is a condition fulfilled by a rectangular hyperbola 
having Ov and Op for the asymptotes, so that the rectangular 
hyperbola is the graphic representation of Boyle’s law.) As 
the volume increases indefinitely the pressure will diminish 
indefinitely and the point P will approach the line Ov but 
will never reach it. Similarly if the pressure be increased P 
will approach the line Op but never reach it. The 
curve thus traced represents the relation between pressure 
and volume for a given mass of air kept at constant tempera¬ 
ture, and is called an isothermal line. 

327. If the substance does not obey Boyle’s law the 
isothermal line will differ from that above described. For 
example, in the case of carbonic anhydride at, say, 15° C., the 
product of the pressure and volume will be very nearly 
constant if the pressure is less than two or three atmospheres, 
and the isothermal line’ will nearly coincide with the corre¬ 
sponding (hyperbolic) line for air, but at higher pressures the 
volume is less than Boyle’s law indicates and the isothermal 
curve for carbonic anhydride falls below the air line. When, 
at length, the pressure is reached at which liquefaction 
commences, the pressure remains constant while the volume 
decreases until the whole mass is liquefied and the isothermal 
line consequently becomes horizontal. As soon as the whole 


206' ISOTHERMALS OF CARBONIC ANHYDRIDE. 

is liquefied the diminution of volume with further increase 
of pressure is comparatively slow and the line slopes upwards 
towards Op at a great and increasing inclination. 

328. When a quantity of vapour is saturated, if the 
temperature is kept constant any diminution of volume 
produces condensation and no increase of pressure can take 
place until the whole has been liquefied. Hence the isother¬ 
mal line of a substance which is partly liquid and partly a 
saturated vapour is necessarily horizontal. When the whole 
of the substance has been liquefied the pressure may have to 
be increased enormously to produce any sensible diminution 
of volume, and the isothermal line becomes nearly parallel to 
Op. This is the case with water at ordinary temperatures 
but there are some liquids which, like liquid carbonic anhydride, 
are extremely compressible when on the point of boiling, and 
the isothermal line for such liquids is at first considerably 
curved but as the pressure is increased the compressibility 
diminishes and the line becomes more nearly parallel to Op. 

329. The accompanying figure shews the isothermals for 
carbonic anhydride corresponding to the temperatures in¬ 
dicated. The dotted line is drawn through all the points at 
wdiich liquefaction commences and terminates, so that all points 
which correspond to the existence of the substance partly as 
liquid and partly as vapour lie below the dotted line. It 
will be noticed that at 13°T C. there is a considerable 
difference between the volume of the substance as vapour 
(or gas) and its volume as liquid; hence the horizontal line, 
within the dotted curve, corresponding to a state partly 
liquid and partly gaseous is of considerable length. At 
21 0, 5 C. the volume of the liquid is much greater while the 
volume of the gas when liquefaction is about to commence is 
much less, so that the portion of the isothermal within the 
dotted curve is much less, and it will be noticed that 
it differs slightly from a horizontal straight line. At 
higher temperatures the difference between the liquid and 
gaseous states is still less and the isothermal of 30° 92 C. 
(not shewn in the figure) just touches the top of the dotted 
curve without cutting it. This point of contact corre¬ 
sponds to the critical point. The isothermals above this 


THE CRITICAL POINT. 


207 


do not meet the dotted curve at all and there is no range over 
which the substance is partly liquid and partly gaseous. In 

Fig. 63. 











208 


ISENTROPIC LINES. 


only then, is it strictly entitled to be called a gas. When in 
the gaseous state at a temperature below the critical point 
it should be called a vapour. It will be noticed that the 
isothermals for some distance above the critical point still 
shew a tendency to contrary flexure just above the dotted 
curve, as though the substance were still inclined to liquefy, 
and the departure from Boyle’s law is very great. At 48°T C. 
however this tendency has quite disappeared and the 
isothermal is more like that of a perfect gas. The isothermals 
of 13°T C., 31°T C. and 48°T C. corresponding to a perfect gas 
whose volume is the same as that of the carbonic anhydride 
at atmospheric pressure are shewn in the top right hand 
corner of the diagram. For carbonic anhydride the pressure 
at which condensation commences at 13°T C. is about 47 
atmospheres; at 21°*5 it is about 60 atmospheres; while the 
critical pressure is nearly 75 atmospheres. 

330. If a quantity of gas be compressed while no heat is 
allowed to enter or leave it, its temperature will be raised on 
account of the compression and the pressure will consequently 
be increased more than if the temperature had been kept 
constant. Hence, if we represent the several conditions 
through which the substance passes by a line on the indicator 
diagram, such a line -will at every point be inclined at a 
greater angle to the line of volumes than the corresponding 
isothermal and hence will cut across the successive isother¬ 
mals (as the temperature of the substance is raised). A line 
representing the relation between the pressure and volume 
of a substance when no heat is allowed to enter or leave it is 
sometimes called an adiabatic line but the term isentropic 
line is preferable. In the accompanying figure the con¬ 
tinuous lines represent isothermals for a perfect gas and the 
dotted lines isentropics. (Fig. 54.) 

331. The indicator diagram was first employed by James 
Watt to indicate the pressure and volume of steam in the 
cylinder of an engine (on one side of the piston) at every 
point throughout the stroke. In Watt’s indicator the pressure 
was registered by a pencil which was attached to a piston 
moving in a very small cylinder to which the steam from the 
engine cylinder had access. The piston was pressed down by 


ISENTROPIC LINES. 



Fig. 54. (Art. 330.) 



G. 


14 








210 


watt’s indicator. 


a spring while the steam gaining access to its lower side forced 
it up against the pressure of the spring. Fig. 55. 

It is well known that in helical springs 
the compression or extension is propor¬ 
tional to the force applied; all spring 
balances are based on this principle: 
hence, the pencil of the indicator was 
raised through a distance proportional 
to the excess of the pressure of steam 
in the cylinder over the atmospheric 
pressure, or if the steam pressure at 
any time were less than atmospheric 
the pencil was depressed through a 
corresponding distance. As it moved 
the pencil traced a line upon a sheet of 
paper attached to a board which could 
be made to move in exactly the same 
way as the piston (though the length of 
the traverse was reduced). If the 
pressure in the cylinder remained con¬ 
stant a horizontal line would be traced by the pencil on 
the moving board, if the pressure increased or diminished 
when the board was stationary, or changed suddenly while 
the board was moving, a vertical line would be the result. 
A steady change of pressure accompanying the change of 
position of the piston would cause a curved line to be 
described. 

332. It was found however that although the traverse of 
the pencil in 'Watt’s indicator was only a lew inches when 
the pressure varied rapidly the kinetic energy acquired by 
the little piston, pencil, &c., was sufficient to carry the piston 
and pencil far beyond the position corresponding ^to the 
steam pressure. This difficulty was obviated by allowing the 
piston to move only through a very small distance, correspond¬ 
ingly strong springs being employed, and the motion of the 
piston was multiplied in the pencil by a system of levers. 
The accompanying figure shews Richards’ indicator in which 
this multiplication is effected by a combination of levers 
similar to Watt’s “parallel motion.” In Dark’s high speed 
indicator the pencil moves in a vertical guide, the lever 

















RICHARDS’ INDICATOR. 


211 


actuating it having a longitudinal slot cut in it to allow of 
this motion of the pencil. In all indicators now in use the 

Fio. 56. 



paper is wrapped upon a cylinder, or drum, which is made to 
revolve through rather less than one revolution by the motion 
of the piston of the engine arid is made to return by a spring 
contained within the instrument. As the stroke of the engine 
is generally much longer than the longest diagram the 

14—2 















































212 


EXPANSIVE WORKING. 


indicator can draw it is necessary to employ some mechanism 
by which the drum of the indicator may be moved through 
a distance less than that of the piston but always strictly 
proportional to it. Springs of different strengths are gene¬ 
rally supplied with the instrument and so arranged that a 
movement of one inch on the part of the pencil corresponds 
to a steam pressure varying from 10' lbs. to 80 lbs. on the 
square inch according to the particular spring employed. 

338. If the steam from the boiler be allowed full access 
to the cylinder during the whole of the forward stroke of the 
piston and the steam in the cylinder is allowed to escape 
freely into the air during the whole of the backward stroke, 
the ports being opened and closed at the instant when the 
piston is at the extreme end of its stroke, the diagram traced 
by the indicator will be a rectangle, the upper side correspond¬ 
ing to boiler pressure and the lower side to atmospheric 
pressure. The diagrams of some steam fire-engines are of 
this character, for in these engines the object is to get as much 
work as possible from the engine in a given time, and that 
regardless of the expenditure of fuel. Hence the full boiler 
pressure of the steam is sustained till the end of the stroke. 

But in all engines in the working of which economy is a 
consideration the “ exhaust steam ” is not allowed to escape 
at full boiler pressure^ but the supply from the boiler being 
cut off long before the stroke is completed the steam in the 
cylinder is made to expand, doing work as it expands, and is 
not allowed to escape until its pressure has been reduced very 
much below that of the steam in the boiler. The accom¬ 
panying diagram may be taken as typical of a high-pressure 
engine working expansively. The line AB represents the 
condition of affairs during the period of admission, and the 
communication being open with the boiler the pressure is 
maintained nearly equal to that in the boiler itself. At B 
the steam port is closed and the steam being confined within 
the cylinder expands as the piston continues its motion, 
tracing out the curve B G until at the point G the exhaust 
port is opened and the steam being allowed to escape the 
pressure falls rapidly almost to atmospheric pressure. At D 
the piston is at the extremity of its stroke, it then returns, 
the indicator tracing out the line DE with the exhaust port 


NORMAL INDICATOR DIAGRAM. 


213 


open until on the piston arriving at D the exhaust port is 
closed and the small amount of steam remaining in the 

Fig. 57. 


A B 



cylinder is compressed so as to form an elastic cushion and 
assist the rebound of the piston. The compression portion of 
the curve is represented by EF, and at F the steam port 
is opened and the pressure rises immediately to nearly the 
full boiler pressure. 

334. A glance at the indicator diagram generally shews 
whether the engine is working properly or whether there is 
anything wrong with the pistons, valves, steam ways, &c. 
For example, a leaky piston would be betrayed by the 
expansion curve falling much more rapidly than is consistent 
with the law of expansion of steam under the conditions 
obtaining in the cylinder. If the steam pipe from the boiler 
is too small, or if the steam port is not opened wide enough 
and quickly enough, when the piston commences its stroke 
the supply of steam will not keep pace with the piston and 
the line corresponding to the period of admission will slope 
downwards from A to B. This limiting of the steam supply 
is called “ wire-drawing ” and the steam is said to be “ wire¬ 
drawn” This effect also occurs in engines which are regulated 
by a “ throttle valve ” opened and closed by the governor. It 
always involves a waste of power and hence it is preferable 
to govern by altering the position of the cut off, B , either by 
controlling the travel of the ordinary slide valve, or by a 
separate “ expansion valve.” Sometimes the wire-drawing is 





214 


INDICATOR DIAGRAMS. 


so marked that the period of admission can scarcely be 
distinguished from that of expansion. 

If the exhaust port does not allow a sufficiently ready 
egress for the steam the line DE instead of practically 
coinciding with the atmospheric line will be considerably 
above it. This shews that some of the work done by the 
steam in expanding is employed in overcoming back pressure 
which detracts from the work done by the engine. 

335. The accompanying diagram is a rough copy of 
one taken from an engine employed in blowing a fan. It 


Fig. 58. 



will be noticed that the compression commences at E y or at 
about one-half stroke, and the piston in its motion from right 
to left compresses the steam in the cylinder until when the 
steam port is opened at F the pressure is considerably greater 
than that of the steam in the boiler, and the first effect of the 
opening of the steam port is the diminution of the pressure 
in the cylinder down to that existing in the boiler. As the 
piston advances the supply of steam is insufficient to keep up 
the pressure in the cylinder and the consequent “wire¬ 
drawing ” is indicated by the downward slope of the admis¬ 
sion line A B. Such a diagram shews that there is a great 
waste of energy accompanying the working of the engine. A 
readjustment of the slide valve making the compression much 
later and opening the steam ports earlier so that there may 
be a wider aperture for the admission of the steam when the 



INDICATOR DIAGRAMS. 


215 


piston advances would enable the engine to do the same 
amount of work with a much smaller supply of steam and 
consequently a smaller consumption of fuel. 

336. If the pressure on the piston remained constant 
the work done during a single stroke of the engine would, of 
course, be equal to the resultant pressure upon the piston 
multiplied by the length of the stroke. In estimating the 
resultant force we must of course take account of the pressure 
on both sides of the piston. Thus, if the area of the piston 
is 80 square inches, the pressure on one side 60 lbs. on the 
square inch (i.e. 45 lbs. above atmospheric pressure), and that 
on the other side 17 lbs. on the square inch, the resultant 
pressure will be equivalent to 43 lbs. on the square inch and 
will be equal to 3440 lbs. on the whole piston. If the 
length of the stroke is 2 feet the work done during the 
single stroke will be 6880 foot pounds. If similar conditions 
obtain during the return stroke the whole work done for one 
revolution of the engine (if it has only a single cylinder) will 
be 13760 foot pounds. 

But instead of considering the pressure on both sides of 
the piston at once it is generally more convenient to credit 
the steam on the one side of the piston with the whole of the 
work it does during the advance and debit it with the 
work which has to be done against the steam pressure on the 
same side during the return of the piston. The balance is 
the amount of useful work obtained from the steam on that 
side of the piston during the complete revolution of the 
engine. The steam on the other side is then treated in the 
same manner. It will be seen presently that this balance, or 
total amount of work done by the steam on one side of the 
piston, is shewn by the indicator diagram for that side. 

337. Suppose, as before, that during the whole of the 
forward stroke of the piston the pressure is constant; and 
constant, but, of course, considerably less, during the return 
stroke. The indicator diagram will then be a rectangle, 
ABCD , and upon a certain scale, the height of its top side 
AB above the line of zero pressure, ON, will represent the 
whole pressure on the piston, while its length will represent, 
also on a particular scale, the length of the stroke. Hence 


216 


INDICATOR DIAGRAMS. 


tlie rectangle ABNO will represent the work done by the 
steam on one side of the piston during the forward stroke. 


Fig. 59. 

A B 






When the piston returns the steam still exerts a pressure, 
represented by NG or .OD, and this opposes the motion of 
the piston so that an amount of work represented by ON-OD 
has to be done against this pressure during the return stroke. 
The difference of these rectangles, viz:—the rectangle 
ABCD, represents the useful effect of the steam on the one 
side of the piston during a complete revolution of the engine, 
and this rectangle is the indicator diagram for one end of the 
cylinder during the stroke. If we add to this the area of the 
diagram for the other side of the piston we obtain the whole 
amount of work done during the stroke. 

338. Now suppose that the pressure is variable and let 
the indicator diagram be ABCD. Draw ON the line 

Fig. 60. 

A B 












INDICATOR DIAGRAMS. 


217 


corresponding to zero pressure and let CN touch the diagram 
at its extreme right. Then ON represents the length of the 
stroke. The work done by the steam while the piston moves 
over a very small portion of its stroke throughout which the 
pressure may, without sensible error, be regarded as constant, 
will be equal to the product of the pressure and the corre¬ 
sponding distance travelled by the piston. Thus, the work 
done during the portion of the stroke represented by ef will 
be represented by the area of the strip efgh and so on for 
other portions of the stroke. Hence the whole work done 
by the steam on one side of the piston during the forward 
stroke will be represented by the area ABC NO and that 
done against the steam during the return stroke by the area 
CNOD. The useful effect will therefore be represented by 
the area of the indicator diagram ABCD. In the figure of 
Art. 335 the area of the little loop at the top must be 
subtracted from that of the rest of the diagram in order to 
shew the work done. 

339. In employing the indicator practically for the 
purpose of determining the rate at which the engine is 
working it is usual to use it simply for the purpose of finding 
the average difference throughout the stroke between the 
pressure of the steam at any point of the forward stroke and 
its pressure at the same point during the return. This is 
represented by the average height of the indicator diagram, 
the average being taken by drawing a great many vertical 
ordinates at equal distances throughout the diagram, and just 
as the area of the diagram is equal to its average height, as 
thus determined, multiplied by its length, (for the process is 
simply equivalent to dividing the diagram into strips and 
taking the sum of the area of the strips,) so the work done by 
the steam on one side of the piston during the complete revolu¬ 
tion of the engine will be equal to the average difference of 
pressure multiplied by the area of the piston and by the 
length of the stroke. 

Sometimes this average difference of pressure, or mean 
effective pressure , as it may be called, is found by measuring 
the area of the diagram with a planimeter and dividing the 
area by the length. The result represents, on the scale of 
the diagram, the mean effective pressure. But the more 


218 


INDICATED HORSE-POWER. 


usual method consists in dividing (in imagination) the 
diagram into a certain number (say ten) of vertical strips 
of equal width and drawing and measuring the middle 
ordinates of these strips. The mean of these ordinates is 
very nearly equal to the mean height of the diagram and 
represents with considerable accuracy the mean effective 
pressure. It is, of course, only necessary to draw these 
middle ordinates and not the lines of division of the strips. 
For example, if ten ordinates are to be drawn we have only 
to divide the length of the diagram into twenty equal parts 
and draw ordinates through the first, third, fifth, &c., points 
of division. This method, clearly, applies equally to con¬ 
densing and to non-condensing engines, the only difference 
being that in the latter class the diagram lies wholly above the 
line of atmospheric pressure while in the former the exhaust 
line may be very little above the line of zero pressure. 

340. The following example will shew how the rate at 
which an engine is working can he determined in horse¬ 
power from its indicator diagram, speed, length of stroke and 
area of piston. It should be noticed that in addition to the 
indicator diagram it is necessary to know the area of the 
piston, the length of its stroke and the number of revolutions 
per minute, or instead of the two latter quantities we may 
substitute the mean velocity of the piston in feet per 
minute. 

The diameter of the piston of a single cylinder engine is 
14 inches , the length of the stroke 30 inches , the number of 
revolutions per minute 50, the indicator diagrams the same 
on both sides of the piston , and the heights of the equidistant 
ordinates correspond respectively to 46J, 50, 50, 36^, 25, 18, 
13, 9, 6, 4 lbs. on the square inch. It is required to find the 
h. p. at which the engine is working. 

The sum of the above differences of pressure is 258 and 
the mean effective pressure is, therefore, 25’8lbs. on the 
square inch. The area of the piston is 497r, or nearly 
154, square inches, and the distance travelled by the piston 
in a minute is 250 feet. Hence the work done per minute 
is 25*8 x 154 x 250 or 993300 foot pounds, and the horse¬ 
power is therefore 9 s 9 3 3 o 3 o 0 o 0 or 30*1. 


DIAGRAM OF PUMPING ENGINE. 


219 


341. If the diagrams obtained on the two sides of the 
piston are not similar the mean effective pressure must be 
found for each side and the mean of these taken. In ordinary 
rotary engines there is not generally much difference between 
the two diagrams, but inasmuch as the shortness of the 
connecting rod necessitates the piston being some distance in 
front of the middle of the cylinder in the forward stroke 
when the crank shaft has turned through a quarter revolu¬ 
tion it follows that there is usually an appreciable difference 
between the diagrams for the front and back of the piston. 
Sometimes with pumping engines nearly the whole of the 
work of forcing the water is done during the return, or down, 
stroke, while in the forward, or up, stroke there is very little 
load on the engine. In such a case the steam is automatically 
cut off as soon as sufficient has been admitted for the work of 
the stroke : (in some engines the cut off occurs as soon as the 
piston has obtained a certain speed). The diagrams will then 
be very different, shewing the difference in the amount of 
work done during the forward and return strokes. The 
accompanying figure represents two diagrams from a pumping 
engine belonging to the Corporation of Nottingham. The 
diagram marked A corresponds to'the top of the piston and 


Fig. 61. 



* 

shews a much greater supply of steam than the diagram B 
taken from the bottom of the cylinder. This is because the 
whole of the work of forcing the water to the reservoir was 
done in the down stroke of the engine while in the up stroke 
the engine had only to raise the water from the well to the 
ram. By attaching a weight to the end of the beam and 








220 


INDICATOR DIAGRAMS. 


compelling the steam to raise the weight during the up stroke 
while the weight assists the steam in the down stroke it is 
possible to balance the engine and make the two diagrams 
alike. The horizontal line in the diagram is the line of at¬ 
mospheric pressure. It is usual to measure steam pressure in 
pounds per square inch above and below atmospheric pressure. 

342. The four accompanying diagrams shew the work done 
by the steam on one side of the piston of a horizontal engine 
with a single cylinder, the governor controlling the travel of a 
separate expansion valve which regulated the cut off according 
to the speed of the engine. The engine was making 50 
revolutions per minute, the diameter of the piston was 14 
inches and the length of the stroke 30 inches. When the 
first diagram was taken the engine was driving only a couple 


Fig. 62 . 




of idle pulleys and consequently had little more than its own 
frictional resistance to overcome. The second diagram was 
taken when the engine was driving a counter-shaft and a 
10-light Brush Dynamo, but no current was being generated 
and the engine had therefore only the mechanical resistances 
of the system to overcome. The electric circuit was then 
completed, the 10 Brush lamps lighted, and the third diagram 
was obtained. A mortar mill and some other machinery was 
then connected with the engine and the fourth diagram was 
the result. When this last diagram was taken the load on 
the engine was rather too great for economic working. 












EXAMPLES. 


CHAPTER I. 

1. Define temperature. When is one temperature said to be higher 
than another ? 

2. When are two bodies said to be in thermal equilibrium ? 

3. What method is adopted in practice to determine whether two bodies 
are in thermal equilibrium or not ? 

4. Give a definition of temperature, and explain accurately how a mer¬ 
curial thermometer is filled and graduated. 

5. Why should a mercurial thermometer be kept for a long while after 
it has been filled before it is graduated ? 

6. Will two thermometers, with tubes of uniform bore, filled with the 
same fluid, and having their freezing and boiling-points accurately deter¬ 
mined, necessarily agree at intermediate temperatures ? 

7. Describe some form of maximum thermometer. 

8. Why is mercury used to fill ordinary thermometers ? 

9. What advantages or disadvantages attend the use of (1) mercury, or 
(2) air, in a thermometer ? 

10. A thermometer is graduated to register at the freezing-point 15° 
and at the boiling-point 125°. What division in it corresponds to 104° F. ? 

Aiis. 59°. 

11. De Lisle’s thermometer registers at the boiling-point 0° and at the 

freezing-point 150°. Find the temperature on the Centigrade scale which 
corresponds to 95° De L. Am. 36|° C. 

12. What temperature is denoted in Fahrenheit’s scale by a number 

twice as large as in the Centigrade scale ? Am. 160° C. = 320° F. 

13. Two thermometers having been made from equal tubes, it is found 

that divisions of the same length serve as a Keaumur scale for one and 
as a Centigrade scale for the other. Compare the quantities of mercury in 
the thermometers. Am. 4:5. 


222 


EXAMPLES. 


CHAPTER II. 

. 1. Explain the difference between temperature and quantity of heat. 

2. What thermal unit is generally employed to measure quantities of 
heat? 

3. Define specific heat, and describe a method by which the specific 
heat of a solid body may be determined. State the precautions required in 
practice, and the method of correcting for loss of heat. 

4. Distinguish between capacity for heat and specific heat. 

5. Does the specific heat of a body generally depend upon its tempera¬ 
ture? 

6. Describe an apparatus by which the quantity of heat given off by 
any substance in cooling from any ordinary temperature to 0° C. may be 
measured. 

7. Describe the method of determining the specific heat of a solid by 
means of a Bunsen’s ice calorimeter, and point out the advantages of this 
method. 

8. Describe Regnault’s method of determining the specific heat of gases 
under constant pressure. 

9. How much coal is required to heat 40 tons of iron through 1000° C., 

supposing a pound of coal in burning to produce 8000 units of heat and the 
specific heat of iron to be *11379 ? Ans. 1274*448 lbs. 

10. If 60 lbs. of mercury at 80° C. are poured into 20 lbs. of water at 

10° C., what will be the temperature of the mixture? Ans. 16 T 4 r ° C. 

11. A pound of water at 200° E. is mixed with a pound of mercury at 

60° F. What will be the temperature of the mixture when it has become 
uniform, supposing that no heat is lost from it ? Ans. 195*5° C. nearly. 

12. One pound of iron, at a temperature of 100° C., is placed in 1*5 lbs. 

of water at 20° C., and when the temperature of the iron and water is the 
same it is found to be 25° C.; find the specific heat of iron. Ans. *1. 

13. Calculate the specific heat of a substance from the following data: 

31*8 grammes heated to 100° C., when immersed in a calorimeter contain¬ 
ing 107 grammes of water at 11*09° C., caused a resulting temperature of 
12*57° C. Ans. *057 nearly. 

14. A piece of metal, weighing 120 grammes, and at a temperature of 

100° C., is immersed in 360 grammes of water at 19 C°. After the tempera¬ 
tures have become uniform that of the water is found to be 22° C. Calcu¬ 
late the specific heat of the metal. Ans. *115. 


EXAMPLES. 


223 


15. The temperature of 300 grammes of iron, whose specific heat is 

•113, is raised to 98° C., and the iron is then immersed in 200 grammes of 
water originally at 12° C. and contained in a copper vessel weighing 80 
grammes. What will be the resulting temperature supposing no heat to 
escape, the specific heat of copper being *095 ? Ans. 24-07° C. 

16. A lump of platinum, weighing 12 lbs., was plunged into a vessel 

containing 10 lbs. of water at 15° C. When the temperature had become 
uniform it was found to be 30° C. Assuming that no heat was lost during 
the experiment, calculate what the temperature of the platinum must have 
been, its specific heat being -032. Ans. 150-2° C. 

17. A pound of iron at 100° C. is placed in a receiver of Laplace’s 
♦ calorimeter, and the water which flows from the apparatus is found to weigh 

•144 lbs. Find the specific heat of iron. Am. *114 nearly. 


CHAPTER HI. 

1. Enumerate the principal sources of heat. 

2. Mention some cases in which chemical action produces a considerable 
quantity of heat. 

3. Explain how the heat produced by an ordinary coal fire has been 
originally derived from the sun. 

4. What condition must be fulfilled by the temperature of the products 
of combustion in order that a substance may continue to burn in air ? Why 
will ammonia burn in pure oxygen but not in air ? 

5. How would you determine the calorific power of a sample of coal ? 

6. Mention some cases in which heat is produced by purely mechanical 
means. 

7. What is the effect of heat upon stretched India-rubber, and what the 
effect on the temperature of a piece of India-rubber of suddenly stretching 
it? 

8. Describe some experiment by which the heating effect of an electric 
current may be rendered apparent. 

9. According to what law does the heat produced by an electric current 
in a wire depend upon the strength of the current and the resistance of the 
wire? 

10. Account for the heat produced by the sudden crystallisation of a 
quantity of salt which has been held in solution. 


224 


EXAMPLES. 


CHAPTER IV. 

1. Define the coefficients of linear, superficial, and cubic expansion of a 
solid, and shew that the coefficients of superficial and cubic expansion may 
be taken as twice and three times that of linear expansion respectively. 

2. Place the following substances in the order of their coefficients of 
expansion: air, alcohol, glass, iron, mercury, water. 

3. Describe Roy and Ramsden’s method of determining the coefficient 
of linear expansion of a metal. 

4. How is it proved that water has a point of maximum density, and 
what natural phenomenon does this account for? 

5. What is the difference between the real and apparent coefficients of 
expansion of a fluid? 

6. Shew how to determine experimentally the coefficient of apparent 
cubic expansion of a liquid contained in a glass envelope. 

7. Describe Dulong and Petit’s mode of determining the absolute coeffi¬ 
cient of expansion of mercury. 

8. Explain how to employ a weight thermometer to determine the cubic 
expansion of a metal rod. Can the method be adopted with all metals? 

9. Describe three forms of compensating pendulums. 

10. Describe the plan adopted on railways in order to prevent variations 
of temperature changing the positions of points which are moved by levers 
at a considerable distance and connected to them by iron rods. 

11. If a line of railway be laid with rails which are 8 yards long at 0°C., 

find the least distance between consecutive rails which will allow of the 
expansion due to an increase of temperature of 30° C., the coefficient of 
expansion of iron being *000012. Ans. *10368 in. 

12. The cubic dilatation of mercury for 1°F. is about *0001, and the 

linear expansion of brass for 1°F. about *00001. A barometer with a brass 
scale correctly graduated at 62° F. reads 30 inches at 47° F. Find the true 
pressure reduced to inches of mercury at 32°F. Ans. 29*950. 

13. The coefficient of expansion of iron-wire is *00001235, and the length 

of wire between a distant signal and the signal-box is 900 yards. If the wire 
has to be pulled through 6 inches to lower the signal, find what increase of 
temperature of the wire will allow the signal to return to danger after it has 
been lowered. Ans. 14*995°, nearly. 


EXAMPLES. 


225 


14. The capacity of the bulb of a thermometer is 500 times that of each 

inch of the tube; the mercury just fills the bulb at 0°C. How far up the 
tube will it stand at 10° C., assuming the coefficient of cubic expansion of 
mercury in glass to be -000155? Am. *775 in. 

15. The specific gravity-of silver at 0°C. is 10 5. Assuming its coeffi¬ 
cient of linear expansion to be -00002, shew that its specific gravity at 
1000°C. is 9*90 (water at 0°C. being taken as the standard). 

16. The time of vibration of a pendulum varies as the square root of its 
length. A clock keeps correct time at 0° C., but loses 37-35 seconds per 
week at 10° C. Find the coefficient of linear expansion of its pendulum. 

Am. -00001235... 


CHAPTER V. 

1. State Boyle’s law, and describe some experiment by which its truth 
may be shewn. 

2. Define the coefficient of cubic expansion. What is its value in the 
case of the more permanent gases? 

3. State the law connecting the pressure and temperature of a quantity 
of gas at constant volume. 

4. Describe Balfour Stewart’s apparatus for determining this relation. 

5. What formula expresses the relation between the pressure and tem¬ 
perature of air at constant volume, and what the relation between the volume 
and temperature at constant pressure? Are the constant coefficients identi¬ 
cal in the two formulae? 

6. State the relations between volume, pressure, and temperature in a 
perfect gas. In what manner does a real gas, such as carbonic anhydride, 
differ from the hypothetical perfect gas? 

7. Describe some form of air thermometer, mentioning its advantages 
and disadvantages. 

8. Do the indications of a mercurial thermometer, properly pointed at 
the freezing and boiling points and uniformly divided, agree with those of 
an air thermometer for all temperatures for which it may be used? Why is 
the scale of the air thermometer considered of great importance? 

9. 250 cub. cent, of hydrogen are measured at 77° F. and 750 mm. 
pressure; what would the gas measure at 0°C. and 760 mm. pressure? 

Am. 226'008..„c.c. 

10. If a gas occupy 1000 cub. cent, at 10° C., what will be its volume at 

100°C. under the same pressure? * Am. 1316-02...c.c. 

15 


G. 


226 


EXAMPLES. 


11. A quantity of air, which occupies l-fflg cub. ft. at 10° C. and under 

a pressure of 30 inches of mercury, is raised to 15° C. and the pressure 
reduced to 29 inches. Find its volume. Arts. l*0913.,.c. ft. 

12. Find the volume at 45° C. and under a pressure of 1500 mm. of 

mercury, of a quantity of air which, at 27° C, and under a pressure of 
760 mm., occupies 10 cub. ft. Ans. 5*3707...c. ft. 

13. A quantity of gas occupies 26 cub. ins. at 60°F. and under a pres¬ 
sure of 29 inches of mercury: how much space will it occupy when the 
temperature has risen to 65°F. and the pressure to 50 inches? 

Ans. 15*23...c. ins. 

14. If the compressed air in a flooded coal-pit occupied 2500 cub. ft. at 
50° F. and under a pressure of 70 ins. of mercury, how much space would it fill 
at 60°F. and under a pressure of 29*5 ins. of mercury? Ans. 6048*65...c. ft. 

15. What will be the volume of 100 grammes of hydrogen at 273° C. 
under a pressure of 1420 mm., assuming that a litre of hydrogen at 0° C. 
under a pressure of 760 mm. weighs *0896 grammes? Ans. 1195*66...litres. 

16. If the air in a fire-balloon be raised to 100° C., the temperature of 
the surrounding air being 0° C., and the volume of the balloon 373 cubic feet, 
shew that the balloon will not ascend if its weight exceed lbs., assuming 
the weight of a cubic foot of air at 0° C. and under atmospheric pressure to 
be 1*2 ozs. 

17. The volume of a bubble of gas generated under water at a depth of 

200 fathoms is of a cubic inch. What will its volume be when it reaches 
the surface, the temperature remaining constant and the height of the water 
barometer being 33 feet? Ans. *01245 c. ins. 

18. A given quantity of gas kept at constant pressure, in being raised 
from 0°C. to 100° C., expands in volume in the ratio of 1 to 1*366. Find 
the absolute zero of the air thermometer on the Centigrade scale. 

Ans. -273*2°...C. 

19. Assuming that 30 cubic inches of air at 0°C. would occupy 41 cubic 

inches at 100° C. under the same pressure, find the position on the Centigrade 
scale of the absolute zero of the air thermometer. Ans. - 272 T 8 T ° C. 


CHAPTEK VI. 

1. Explain the terms “unit of heat,” and “latent heat of fusion.” 

2. What becomes of the heat absorbed by a body in changing its state 
from the solid to the liquid, or from the liquid to that of vapour? 

3. How is the latent heat of water determined? 


EXAMPLES. 


227 


4. Find the least quantity of water at 0°C. which, surrounding a pound 
of solid mercury at its freezing point, - 39° C., will just melt the mercury 
without altering the temperatures of either substance, assuming the latent 
heat of fusion of water and mercury to be 79*5 and 2*8 respectively. 

Ans. 246'54...grains. 

5. Find also the ultimate common temperature of the ice and mercury, 

their specific heats being \ and respectively. 4ns. -25*44°...C. 

6. What is the effect of pressure upon the melting points of ice, paraffin, 
cast-iron, lead, gold, and type metal? 

7. How do you explain the fact that two pieces of ice floating in contact 
on the surface of water will freeze together? 

8. When is a liquid said to boil? 

9. State the laws of evaporation, and explain the meaning of the asser¬ 
tion that one gas or vapour acts as a vacuum to another. 

10. Explain the nature of ebullition. What circumstances influence 
the temperature at which it takes place? 

11. How may the height of a mountain be measured by means of boil¬ 
ing water and a thermometer? 

12. Define the quantity called the latent heat of steam at 100° <7., and 
describe a method by which it may be determined. 

13. Water which is boiling freely in an open vessel is suddenly shut in 
by an air-tight lid; what follows? 

14. In a closed vessel is contained water which has cooled so that ebul¬ 
lition has ceased. How may the water be made to boil again without apply¬ 
ing heat to the vessel? 

15. Regnault found the “total heat ” of the vapour of water at i°C. to 
be 605-5 + 0'305£. Explain the meaning of this statement. 

Water boils on the top of Mont Blanc at 85° C. Find the latent heat of 
steam there. Ans. 54^T - 425. 

16. Describe a simple experiment shewing that the pressure of aqueous 
vapour at a constant temperature cannot exceed a certain amount. 

17. How would you expect a liquid to behave when heated to the boiling 
point, if the latent heat of evaporation were zero ? 

18. What is the dew-point, and how is it determined? 

19. State Dalton’s laws for the formation of vapour, and shew how to 
verify them experimentally. 

20. Describe Dalton’s method of determining the tension of aqueous 
vapour between 0°C. and 100° C. 


lo—2 


228 


EXAMPLES. 


21. Explain the cooling action of- a draught of air. 

22. What is meant by the hygrometric state of the air ? Explain how 
it is determined by means of Daniell’s dew-point hygrometer. 

23. What are the laws followed by saturated and non-saturated vapours 
respectively ? 

24. Describe the wet bulb thermometer. What processes are going on 
in the air round the wet bulb ? What practical use is made of this ther¬ 
mometer ? 

25. Explain the action of Wollaston’s cryophorus. 

26. By what method has the increase of pressure of a given volume of 
air when raised from 0°C, to 100° C. been determined? How would the 
presence of water in the vessel affect the result of the experiment ? 

27. Explain how advantage may be taken of the spheroidal state of a 
volatile liquid in order to freeze water or mercury in a red-hot vessel. 

28. How do you account for the apparently serrated form sometimes 
assumed by liquids when in the spheroidal condition ? 

29. Explain a process by which intense cold can be produced by means 
of carbonic anhydride. 

30. Describe Dr Andrews’ experiments on the connection between the 
gaseous and liquid states in the case of carbonic anhydride. 

31. Trace the changes in volume of a pound of ice as it is gradually 
heated under normal atmospheric pressure from - 20° C. to 120° C. 

What are the quantities of heat required during each successive rise of 
10° C. during the process ? 

32. Seven pounds of iron at 100° C. are placed upon a mass of ice at 

0° C. The specific heat of iron being -113, and the latent heat of water 79*5, 
how much water will be produced? Ans. *995 lbs. nearly. 

33. The latent heat of fusion of ice being 79’5, if 1 lb. of ice at 0° C. be 

dropped into 2 lbs. of water at 15*5 C., how much of it will remain un- 
melted ? Ans. lbs. 

34. If 10 lbs. of ice, originally at - 10° C., are boiled away at ordinary 

pressure, find the amount of heat required, having given that the specific 
heat of ice is *5, the latent heat of fusion 79-25, and the latent heat of 
vaporisation of water at 100° C. is 537. Ans. 7212-5. 

35. Given that the latent heat of evaporation of water at 100° C. is 537, 

find how many pounds of steam at 100° C. must be blown into 50 lbs. of 
water at 20° C. to make the water boil. Ans. 7-448... 


EXAMPLES. 


229 


36. If lflbs. of ice at 0°C. be dropped into lib. of water at 100°C., 

what will be the resulting temperature of the mixture, and of what will it 
consist? Ans. 0°C.; 2*2578... lbs. water and *3421... lbs. ice. 

37. The specific heat of ice is *504. The air and everything else in a 

certain room is at 0°C., and a pound of ice at -10°C. is placed in a vessel 
in the room, and water at 12° C. is slowly poured upon it. It is found that 
7*045 lbs. of water are required to just melt the ice. Find the latent heat of 
fusion of water. Ans. 79*5. 

38. How much steam at 100° C. must be passed into 100 lbs. of water 

at 0°C. to raise the whole to 50° C., supposing the whole of the steam con¬ 
densed in the water ? Ans. 8*517... lbs. 

39. What amount of steam at 100° C. must be passed into 100 lbs. of 

water at 0° C., in which 10 lbs. of ice are floating, in order to raise the tem¬ 
perature of the whole to 50° C.? Ans. 10*724... lbs. 

40. How many pounds of iron at 200° C. must be placed in a vessel 

containing 10 lbs. of ice at -10° C. in order to convert all the ice into steam 
at 100° C., the capacity for heat of the vessel being equal to that of 2 lbs. of 
water, and no heat being supposed to escape ? Ans. 657*7... 

41. The barometer stands at 30 inches, the thermometer at 20°C., and 

the dew-point is 15° C. The maximum pressure of aqueous vapour at 15° C. 
is *508 inches. What portion of the pressure indicated by the barometer is 
due to aqueous vapour? Ans. *01693... of the whole pressure. 

42. What is the weight of 100 cubic centimetres of damp oxygen collected 

over water at 20° C. under a pressure of 760 mm., it being given that a litre of 
hydrogen at 0°C. and under a pressure of 760 mm. weighs *0896 grammes, 
the densities of oxygen and aqueous vapour compared with hydrogen as 
unity are respectively 16 and 9, and the maximum pressure of aqueous 
vapour at 20°C. is 17*7 mm.? Ans. *1321... grammes. 

43. Calculate the weight of a litre of hydrogen collected over water at 

20° C., the barometric pressure being 765 mm., assuming that a litre of 
hydrogen at 0° C. and under a pressure of 760 mm. weighs *0896 grammes, 
the density of aqueous vapour is 9 times that of hydrogen at the same tem¬ 
perature and pressure, and the maximum pressure of aqueous vapour at 
20° C. is 17*4 mm. Ans. *099325 grammes. 

44. A closed tube, 20 inches long, containing dry air at a pressure of 

30 inches of mercury, is separated into two equal parts by a narrow piston. 
As much water as will evaporate is then introduced into one portion of the 
tube, the temperature of the whole being maintained at 64° F. How far 
will the piston move, the maximum pressure of aqueous vapour at 64° F. 
being assumed to be *6 in. ? Ans. *099... in. 


230 


EXAMPLES. 


CHAPTEE VII. 

1. Foe what purposes is iron comparatively useless in fire-proof struc¬ 
tures, and why ? 

2. What is meant by tempering , as applied to steel? 

How would you temper a graver for cutting iron ? 

3. What is the effect qf heating and suddenly cooling a piece of copper? 
What influence has hammering upon the mechanical properties of copper 

and brass ? 

4. What is the effect of heating a magnet (1) through three or four 
degrees, (2) to a red heat, and then allowing it to cool ? 

5. What influence has increase of temperature on the electrical resist¬ 
ance of (1) metallic conductors, and (2) electrolytes ? 

6. What is the Peltier effect ? 

Why is it generally not advisable to employ a very strong current in 
order to shew the Peltier effect ? 

7. According to what law does the electro-motive force of a thermo¬ 
electric couple depend upon the temperatures of the junctions? 

8. What is meant by thermo-electric inversion ? 

Describe an experiment illustrating this inversion. 

9. Describe some form of thermo-electric pile. 


CHAPTEE VIII. 

1. Give a short description of the three methods by which heat is con¬ 
veyed from one place to another. Distinguish carefully between convection 
and radiation. 

2. How would you compare the thermal conductivities of two good con¬ 
ductors of heat? 

3. Two equal bars of different metals are coated with wax, and one end 
of each exposed to the same source of heat. Why cannot we compare their 
thermal conductivities by observing the time required to melt the wax to a 
given distance along each ? 

4. Define the thermal conductivity of a substance, and shew how it 
depends on the various fundamental units. Hence, find the requisite factor 
for changing the measure of the thermal conductivity of a substance from 


EXAMPLES. 


231 


pound, foot, minute, Fahr., into gramme, centimetre, second, C., supposing 
1000 grammes to be equal to 2£ lbs., and 30 centimetres to one foot. 

Am. ££. 

5. Give an account of Principal Forbes’ investigation of tbe thermal 
conductivity of wrought iron at different temperatures. 

6. How may it be shewn that the conductivity for heat varies in differ¬ 
ent directions in the same crystal ? 

7. How may it be proved experimentally that water is a bad conductor 
of heat? 

Explain how the temperature of water is raised when heat is applied 
beneath it. 

8. Explain how buildings may be warmed by convection of heat in 
water. 

9. Shew what part is played by convection-currents in causing the 
North-West of Europe to be warmer than the places in the same latitude 
on the East coast of America. 

10. At what temperature does water under ordinary circumstances 
attain its maximum density? 

How may this temperature be experimentally determined ? 

11. The specific thermal conductivity of wrought iron, a second and an 
inch being the units of time and space, is *001. Calculate the number of 
units of heat transmitted per hour through each square foot of the plates of 
a steam-boiler constructed of -§ in. boiler-plate, the temperature of the 
inner surface being kept at 120° C. and that of the outer at 100° C. 

Ans. 27648. 

12. A certain boiler exposes 60 square feet of surface to the action of 
the fire. If the average thickness of the plates be fin., and the outside be 
maintained at 140°C. while the temperature of the inside is 130° C., find 
how many pounds of water can be evaporated per minute, the latent heat of 
steam at 130°C. being 516, and it being given that 6 units of heat pass per 
minute through an iron plate, a foot square and an inch thick, when the 
temperature of one side is 13o 0, 5C., and that of the other 134° *5 C. 

Ans. 11^-lbs. 

13. If S units of heat flow per second through an iron cube of one foot 

edge when one face is maintained at a temperature always 1°C. above that 
of the opposite face, and no heat enters or leaves the remaining faces, how 
much heat will flow in one hour through a boiler-plate 4 feet long, 2 feet 
wide, and half an inch thick, when one face is in contact with boiling water 
and the other with melting ice, supposing the faces of the plates to possess 
the temperature of the water and ice respectively? Am. 69120000. S. 


232 


EXAMPLES. 


CHAPTER IX. 

1. Describe experiments which shew that radiant heat obeys the same 
laws of reflection and refraction as light. 

2. State your reasons for believing that the radiant energy which pro¬ 
duces heat in bodies is of the same nature as light. 

3. State Newton’s law of cooling. Did the experiments of Dulong and 
Petit justify this law? 

4. Describe an experiment which shews that good radiators are good 
absorbers. 

5. By what experiments has the identity of the radiating and absorbing 
powers of bodies been established ? 

6. A blackened cubic vessel of boiling water is so placed that one sur¬ 
face radiates towards a plate of glass and another towards a plate of rock- 
salt. Describe the effects produced. 

How would they be modified if the vessel were replaced by a body at a 
white heat? 

7. How do you explain the apparent radiation of cold ? 

8. Explain fully what happens when a piece of ice is placed in one focus 
of a concave reflector and the bulb of a thermometer in the conjugate focus, 
the temperature of the room and of the thermometer being at first the same 
and higher than that of the ice. 

9. Briefly describe the constituents of the radiation from the carbon 
points of an electric lamp when at a white heat. 

10. What portions of the radiation can pass through rock-salt, crown- 
glass, and quartz, respectively? 

11. Why does the air inside a green-house get so much heated by the 
sun? 

12. In the Artie regions the sun has been known to melt the pitch on 
a ship’s side while the air has been much below the freezing-point. Explain 
this phenomenon. 

13. How is it that ice can be formed at night in the Sahara ? 

14. Give a brief sketch of Prevost’s theory of exchanges. 


EXAMPLES. 


233 


CHAPTER X. 

1. Explain the production of land and sea breezes. 

2. How do you account for the Trade-winds ? 

3. Why is Moscow much colder in winter than Edinburgh ? 

4. Mention some means by which clouds may be produced. 

How do you account for the heavy rain-fall in mountainous districts ? 

5. Does the presence of a cloud apparently clinging to the top of a 
mountain prove that there is no wind there ? 

How do you account for such clouds ? 

6. What is hoar-frost, and how is it produced ? 

Explain the difference between white and black frosts. 

7. What is dew ? 

How is the deposition of dew affected by the state of the sky and the 
nature of the exposed surface ? 


CHAPTERS XI. AND XII. 

1. What is meant by the energy of a system, and by the principle of 
the conservation of energy ? 

2. Distinguish between potential and kinetic energy. 

3. State some of the arguments in favour of the dynamical nature of 
heat. 

4. Describe the experiment which led Rumford to conclude that heat is 
motion. 

5. Define the mechanical equivalent of heat. 

6. Find how many units of heat are required to raise a mass of 80 tons 
to a height of 60 feet. 

7. What assumption was made by Mayer in his determination of the 
Mechanical Equivalent of Heat ? 

8. Why does the specific heat of a gas at constant pressure differ from 
its specific heat at constant volume ? 


234 


EXAMPLES. 


9. How do Dr Joule’s experiments enable us to determine the specific 
heat of air at constant volume, its specific heat at constant pressure being 
known? 

10. How has the relation between the specific heat of air at constant 
pressure and at constant volume been determined? 

11. If a quantity of air be compressed without allowing heat to leave it 
its temperature is raised, while if it be allowed to expand without receiving 
heat its temperature falls. Explain this in accordance with the dynamical 
theory of gases. 

12. Given the specific heat of a gas at constant volume and its specific 
heat at constant pressure, shew how to deduce the mechanical equivalent of 
heat. 

13. Give a brief sketch of the molecular theory of gases, and in accord¬ 
ance with this theory explain why a gas becomes cooled when it expands 
under pressure. 

14. What do you understand by a heat engine? 

15. Explain the term efficiency as applied to heat engines, and state on 
what the efficiency of a reversible engine depends. 

16. Give a very brief account of the principle of the dissipation of energy. 

17. How much mechanical energy is necessary to melt a pound of ice 
at 0°C. ? 

18. The specific heat of lead is -031, and its latent heat of fusion is 5*37; 
what is the mechanical equivalent of the heat required to raise 1 lb. of lead 
from 300°C. to its melting point, 326°C., and to melt it? 

Ans. 8584-64 ft. lbs. 

19. A lead bullet strikes an iron target with the velocity which it would 
acquire in falling freely from rest through 12500 feet. If the whole of the 
velocity of the bullet be destroyed by the blow, and if 95 per cent, of the heat 
generated reside in the bullet, find the temperature to which it will be raised, 
its specific heat being *03 and its initial temperature 30°C. Ans. 314-7°...C. 

20. The melting point of lead is 326° C., its specific heat is *03, and its 

latent heat of fusion 5-37. What is the least height from which a piece of 
lead originally at 20° C. must be allowed to fall upon an inelastic plane in 
order to melt it, supposing 80 per cent, of the heat generated by the blow to 
be produced within the lead? Ans. 25280-625 feet. 

21. Given that 100 cubic inches of a certain gas at 0°C. and under a 
pressure of 15 lbs. weight per square inch weigh 30 grains, and that the 


EXAMPLES. 


235 


specific heat at constant volume is '183, while the specific heat at constant 
pressure is 1*42 times this amount, find the mechanical equivalent of heat, 
assuming that the gas expands by of its volume at 0°C. for each incre¬ 
ment of 1°C. in temperature, the pressure being kept constant. 

Ans. 1390 , 02...ft. lbs. 

22. A certain steam-engine utilises 8 per cent, of the heat generated by 
the combustion of its fuel. The heat generated by the combustion of lib. of 
coal will convert 16 lbs. of water at 100° C. into steam at the same tempera¬ 
ture, the latent heat of steam being 537. A horse can work for six hours a 
day at the rate of of one horse-power. If coals cost 18s. per ton, and the 
maintenance of a horse Is. per day, compare the expense of horse-power 
with that of steam, neglecting the wear of the engine and horse. 

Ans. 12*009... : 1. 

23. If the temperature of steam from the boiler of an engine of 10 horse¬ 
power be 200° C., and if the temperature of the condenser be 80° C., how many 
units of heat must leave the boiler per hour if the efficiency be one-fifth of 
that of a reversible engine working between the same limits of temperature ? 

Ans. 280757 nearly. 

24. What is meant by superheated steam, and what is the use of super¬ 
heating steam in a high pressure engine ? 

25. What is the use of a steam jacket around the cylinder of an engine ? 

26. How do you account for the freezing up of the ports of engines 
worked by compressed air ? 

The exhaust air from an engine driven by compressed air sometimes 
produces a cloud of snow where it escapes from the exhaust port. Explain 
this. 

27. What becomes of the latent heat of evaporation when water 
evaporates ? 

28. -Describe the essential difference between a condensing and a non¬ 
condensing engine. What is a compound engine, and what are its special 
advantages ? 

29. How do you account for the efficiency of a good gas engine being 
greater than that of a steam engine ? 

30. What do you understand by the statement that the mechanical 
equivalent of heat is 424 kilogrammetres ? 

31. When one pound of hydrogen combines with eight pounds of oxygen 
it produces nine pounds of water; how many foot-pounds of work must be 
done in order to decompose one pound of water into its elements ? 


236 


EXAMPLES. 


32. What is meant by the statement that the specific heat of saturated 
steam is negative ? What practical bearing has this fact in connection with 
the steam engine ? 

33. Give a brief sketch of the dynamical theory of gases, explaining the 
cause of the difference between the specific heat of a gas at constant pressure 
and its specific heat at constant volume. 

34. Give a sketch of a normal indicator diagram of a non-condensing 
engine, working expansively and cutting off the steam at the end of one 
quarter of the stroke. 

35. What is an isentropic line ? 

How are the isentropic lines of a gas related to the isothermal lines ? 

36. What is the difference between the expansion line on an indicator 
diagram when the cylinder is jacketed, and when no precautions are taken 
to keep up the temperature of the expanding steam ? 

37. What is the difference between the isothermal lines of 20° C. for a . 
quantity of dry air and for the same quantity of air in the presence of water, 
it being given that the maximum pressure of aqueous vapour at 20° C. 
is 17-4 mm. ? 

What will be the form of the isothermal in the latter case ? 

38. Explain the principle of the indicator, and shew how the indicator 
diagram may be utilised in determining the H. P. at which an engine 
is working. What information respecting the engine must be provided in 
addition to the indicator diagram ? 

39. What difference would you expect to find between the indicated 
H. P. of an engine, and that determined by applying a brake to the fly-wheel, 
and what is the cause of the difference ? 

40. How is the superheating of the steam in a locomotive engine 
generally effected ? 

41. The mean effective pressure of the steam on the piston of an 
engine possessing a single steam cylinder, is 26 lbs. per square inch; the 
diameter of the piston is 6 inches, and the length of the stroke 12 inches ; 
the engine makes 200 revolutions per minute. Find its indicated horse-power. 

42. A quantity of air and a quantity of carbonic anhydride possess the 
same volume at 15° C. under ordinary atmospheric pressure. The pressure 
is then steadily increased to 40 atmospheres; make a sketch shewing the 
difference between the isothermal lines for the two substances. 


EXAMPLES. 


237 


MISCELLANEOUS EXAMPLES. 

1. Distinguish between saturated and unsaturated vapours. What is 
the effect of compressing unsaturated (or superheated) steam, (i) when its 
temperature is kept constant, (ii) when no heat is allowed to enter or 
leave it ? 

2. What is meant by the Thomson -effect in thermo-electricity ? 

3. Why is it that a sprinkling of snow is sometimes observed to lie on 
the exposed surfaces of the sleepers of a railway, but not on the ballast ? 

4. What is the effect of heating (i) a piece of copper, (ii) a piece of steel 
to redness, and then plunging it in cold water ? 

5. How does the coefficient of expansion of water vary between 0°C. 
and 100° C. ? 

6. Explain why a deposit of moisture is sometimes formed on the walls 
of rooms heated by hot water pipes, but not when the rooms are heated by 
open fires. 

7. A quantity of water is distilled at a uniform rate of 5 lbs. per hour 
by water, which flowing uniformly enters the vessel surrounding the worm 
of the still at a temperature of 10° C., and leaves it at a temperature of 
25° C. Find the rate of flow of the water. 

8. Trace the changes in volume which a block of ice at -10° C. under¬ 
goes in being converted into steam at 100° C. 

9. How do you account for the fact that when two equal bars of dif¬ 
ferent metals are covered with wax, and heated equally at one end, some¬ 
times the wax at first melts most rapidly on one of the bars, but after 
a short time the melting proceeds most rapidly on the other bar ? 

10. How is the temperature of boiling water, and of the steam produced 
affected by, (i) a change of atmospheric pressure, (ii) a salt dissolved in the 
water, (iii) a stream of air-bubbles rising through the water, (iv) long boiling 
in a glass vessel ? 

11. State the conditions of evaporation. A closed vessel containing 
water and air at a pressure less than that of the atmosphere is raised to, and 
maintained at, the temperature of 100° C. What determines the cessation of 
boiling, and what the cessation of evaporation ? 

12. If the coefficient of cubic expansion of the liquid in a thermometer 
is less than that of the solid envelope, what effect will be produced on 
heating the instrument ? 


238 


EXAMPLES. 


13. The moistness, or humidity, of the air does not depend solely 
on the amount of aqueous vapour present in it. Explain this statement, 
and point out the conditions on which the humidity of the air depends. 

14. Calculate the weight of 1 litre of hydrogen collected over water at 
20° C., the atmospheric pressure being 765 mm., it being given that 1 
litre of hydrogen at 0°C. and 760 mm. pressure contains *0896 gramme, 
and the pressure of aqueous vapour at 20° C. is 17‘4 mm. 

15. Radiation from (i) an electric lamp, and (ii) a red hot metal ball 
is passed respectively through the following substances :—a plate of glass, a 
solution of iodine in carbon disulphide, a plate of rock salt, a tube of 
dry air, and a tube containing a mixture of air and aqueous vapour. 
Describe the action of each of these media on the radiation from each source. 

16. Water if kept perfectly still may be cooled several degrees below 
0° C. without freezing, but if it be then agitated a portion assumes the solid 
state. Explain why the whole does not become solid. 

17. A heated metal bar is placed upon a metallic support in the middle 
of a room. State all the different ways in which the bar loses heat, 
and carefully distinguish between them. 

18. Describe how you would proceed in order accurately to determine 
the boiling point of a liquid. 

19. How many pounds of carbon must be burnt in order to produce heat 
sufficient to convert 10 lbs. of ice at - 5°C. into steam at 100°C., it being given 
that the heat of combustion of carbon is 8080 units ? 

20. Distinguish between the transmission of temperature and the trans¬ 
mission of heat along a bar. 

21. Account for the laws of evaporation in accordance with the dynamical 
theory of the constitution of bodies. 

22. Mention some bodies which assume a plastic condition in passing 
from the solid to the liquid state. Of what special value is this property in 
the case of those metals which possess it ? 

23. Supposing the section of the mercury tube in Bunsen’s calorimeter 
to be one square millimetre and that the mercury undergoes a displacement 
of 5 centimetres after introducing into the calorimeter 4 grammes of iron at 
90°C., find the specific heat of the iron. 

24. Can hot water be raised to the same height as cold water by means 
of an ordinary pump ? If not what condition determines the height to which 
the hot water can be raised ? 


I N D E X. 


The numbers refer to the pages. 


Absolute expansion of mercury, 57; 
temperature, 74, 197; units, 181, 
182; zero, 74. 

Absorbing and radiating powers, 
equality of, 159. 

Absorption of heat, relation of, to 
radiation, 152, 163; selective, 152— 
154, 156; table of, for gases, 155; 
by iodine solution, 155; by dia- 
thermanous bodies, 164. 

Adiathermanous bodies, 132. 

Air, coefficient of expansion of air, 
&c., 73; comparison between spe¬ 
cific heat at constant pressure and 
constant volume, 83; cooling, by ex¬ 
pansion, 189, 193; determination 
of increase of volume of, 72; dia¬ 
thermancy of, 155; liquefaction of, 
113; relations between pressure, 
volume and temperature of, 72— 
80; specific heat of, at constant 
pressure, 35; at constant volume, 
195. 

Air thermometer, 17, 73, 74, 77, 
83; advantage of, 17, 80. 

Alcohol and water, specific heat of, 
109; thermometer, 15, 17. 

Amounts of heat, 24. 

Andrews, apparatus for the lique¬ 
faction of gases, 112; on the criti¬ 
cal point, 115, 116, 206; table of 
critical temperatures and pressures, 
116. 

Annealing, 123, 124. 

Ansell’s fire-damp indicator, 86. 

Aqueous vapour, table of pressure of, 
105. 

Areometric, method of determining 
expansion, 59. 


August’s psychrometer, 104. 

Availability of Energy, 198. 

Bacon,Lord, on the nature of heat, 185. 

Barometric column, standard height 
of, 7. 

Black, Dr, theory of latent heat, 108. 

Black-frost, 176. 

Boiling under diminished pressure, 
99, 118. 

Boiling point, 97; effect of pressure 
on the, 7, 98, 100; of dissolved 
salts, &c., on the, 9. 

Boiling water, Dufour’s experiment, 
98. 

Bologna flasks, 125. 

Boyle’s law, 71; deviation from, 80. 

Breezes, land and sea, 171. 

Breguet’s metallic thermometer, 69. 

Britannia bridge, 64. 

Bunsen’s calorimeter, 32; burner, 
167. 

C. G. S. units, 181. 

Cagniard de la Tour, on the critical 
point, 114. 

Cailletet, liquefaction of gases, 113. 

Calibration of thermometer tubes, 

12 . 

Calorie, 24. 

Calorimeter, 29, 31, 40, 167. 

Calorimetry, 26. 

Capacity for heat, 25, 136. 

Capillary action, 49. 

Celsius, thermometric scale of, 10. 

Centigrade thermometer, 10. 

Charles’ law, 74. 

Chemical affinity, effect on pressure 
of vapour, 95. 


240 


INDEX. 


Cloud, 173. 

Coal, heat of combustion of, 41. 

Coefficient of expansion, 54. 

Cold, produced by fusion, 87; evapo¬ 
ration, 108; expansion of gases, 81; 
apparent radiation of, 162. 

Colours in spectra from hot bodies, 
148. 

Combustion, heat of, 38; table of, 
41; calorimeters for measurement 
of, 40; temperature of, 39. 

Compensation balance wheels, 68; 
pendulums, 66—68; for expansion 
of railway connecting rods, 70. 

Compensating measuring bars, 65. 

Compression, heat generated by, 42, 
81. 

Condensation, 92, 101, 111. 

Conduction of heat, 131—142; in 
crystals, &c., 140; by water, 143. 

Conductivities, thermal, compared, 
133, 141. 

Conductivity, definition of, 137. 

Conservation of energy, principle of 
the, 184; Newton’s statement of 
the, 182. 

Contraction, accompanying solidifi¬ 
cation, 88; of iron on cooling, force 
of, 63; of india-rubber, 43; practi¬ 
cal application of, 62; strains pro¬ 
duced by, 64, 124. 

Convection of heat, 131, 143—146; 
currents, 148—146. 

Cooling, laws of, 161; Dulong and 
Petit’s experiments on, 161. 

Critical point, 114—117; passage of 
carbonic anhydride through, 117, 
206. 

Crooke’s radiometer, 168. 

Cryophorus, 96. 

Crystallization, heat developed by, 
45, 91; of supersaturated solutions, 
45. 

Crystals, expansion of, 140; conduc¬ 
tion of heat in, 140. 

Cube, Leslie’s, 157. 

Cubic expansion, 53; measurement 
of, 55, 59; of liquids, 56; of gases. 
71. 

Currents, thermo-electric, 127—130; 
electric (as source of heat), 37, 44. 

Cycle, reversible, 197. 

Dalton on pressure of aqueous vapour, 
95; on rate of evaporation, 101. 


Dalton’s laws of evaporation, 93,100, 
107; experimental proof of, 93. 

Daniell’s dew-point hygrometer, 103. 

Dark radiation, absorption of, 152— 
155; polarization of, 157; reflection 
of, 150—152; refraction of, 155. 

Davy, on heat produced by friction of 
ice, 188. 

Davy’s safety lamp, 142. 

Density, maximum, of water, 60,145. 

Despretz’s apparatus for conduction 
of heat, 141. 

Dew, 103, 176. 

Dew-point, definition of, 102; instru¬ 
ments, Daniell’s, 103; Dine’s, 103; 
Regnault’s, 104. 

Diagram indicator, see Indicator 
diagram. 

Diathermancy of air, 158. 

Diathermanous bodies, 132. 

Differential thermometer, 80. 

Diffusion of gases, 85, 86; Graham’s 
law of, 86. 

Digester, Papin’s, 102. 

Dilatation, see Expansion. 

Dine’s dew-point instrument, 103. 

Dissipation of energy, 198. 

Distillation, 96. 

Drops, Prince Rupert’s, 124. 

Drummond’s measuring bars, 65. 

Dry and wet bulb hygrometer, 104. 

Dufour’s experiment on boiling water, 
98. 

Dulong and Petit’s experiments on 
cooling, 161. 

Duprb and Page, on specific heat of 
alcohol and water, 109. 

Dyne, 182. 

Earth, internal heat of, 37, 46. 

Ebullition, 97. 

Ebullition under diminished pres¬ 
sure, 99. 

Efficiency of engines, 181, 185, 199. 

Elastic body, definition of, 48. 

Elasticity, effects of heat on, 123. 

Electric currents, 37, 44; thermo-, 
127. 

Electric pyrometer, 85, 126; resist¬ 
ance, effect of increase of tempe¬ 
rature upon, 125. 

Electrolytes, 125. 

Ellicott’s pendulum, 66. 

Energy, availability of, 197; connec¬ 
tion between it and heat, 186 et 


INDEX. 241 


seq.; conservation of, 182 et seq.; 
definition of, 179; dissipation of, 
198; of mechanical system, &c., 
37, 42—44; kinetic, 179; potential, 
179; radiant, 147—170; transfor¬ 
mation of, 132, 180; units of, 177, 
181. 

Engine, Hero’s, 118. 

Engines, efficiency of, 196, 199; heat, 
193, 196; reversible, 197; con¬ 
densing, 200; Newcomen’s, 200; 
Watt’s, 200; expansive working of, 
200 . 

Erg, 182. 

Ether, latent heat of, 109. 

Evaporation, cold produced by, 111, 
112,118; compared with ebullition, 
97,100; dependent on temperature, 
100; latent heat of, 108; of liquids, 
&c., 92, 93; laws of, 93; rate of, 101. 

Exchanges, Prevost’s theory of, 162 
et seq. 

Expansion, apparent, 12, 55; co¬ 
efficient of, definition, 50, 53; cor¬ 
rections for, 65, 70; comparison 
between easily liquefied and other 
gases, 80; cubic, 53, 59; general 
effect of heat, 4; linear, 50—53; 
allowed for, 64; of gases, 71—75, 
79, 82; of gases, table, 79; of 
water, 59; of gases, cold produced 
by, 82; of certain substances on 
cooling, 50, 85; coefficient of abso¬ 
lute, 57,58; of metals, difference in, 
69; method of measuring, 56; of 
mercury, practical applications of, 
62, 83; relation between coefficients 
of linear and cubic, 54; of solids, 
50; water on cooling and freezing, 
60, 61. 

Fahrenheit’s thermometric scale, 11. 

Faraday, freezing water, &c., in white 
hot crucible, 118; on cold produced 
by evaporation, 112; critical point, 
115; liquefaction of gases, 111. 

Favre and Silbermann’s Calorimeter, 
40. 

Flame, constitution of, 166. 

Flow of heat along a bar, 134; across 
a plate, 137. 

Fluids, definition of, 48. 

Fluorescent substances, i53. 

Fog, 174. 

Foot-pound, 165 ; poun&al, 177. 


Forbes’ experiments on conductivity 
of wrought iron, 140, 141. 

Freezing mixtures, 112; water in 
white hot crucible, J18. 

Freezing point, effect of increase of 
pressure on, 89, 90. 

Friction, heat developed by, 42, 190. 

Frost, 93, 120. 

Fuel, heat of combustion of, 41. 

Fusion, of ice, specific heat measured 
by, 31, 32; latent heat of, 30, 108; 
laws of, 91. 

Galvanometer, 117, 128, 148. 

Gas flame, nature of, 166. 

Gas, perfect, 79; distinction between 
gas and vapour, 92. 

Gaseous laws, the, 74; examples of, 
78; deviation from, of easily lique¬ 
fied gases, 79; application to va¬ 
pours above dew-point, 105. 

Gases, condensation of, 111; convec¬ 
tion of heat in, 143; connection be¬ 
tween temperature and pressure of, 
76; cold produced by expansion, 82; 
defined, 49, 71; diffusion of, 85, 
86; effects of heat upon, 74; ex¬ 
pansion of, 71—75, 79, 82; heat 
generated by compression of, 81; 
liquefaction of, 111; molecular 
theory of, 49, 78, 86,106; pressure 
of, explained by Dynamical theory, 
79; specific heat of, 33, 82; table 
of coefficients of expansion, 79. 

Gay Lussac’s law, 74; on pressure of 
aqueous vapour, 95. 

Glaciers, motion of explained by rege¬ 
lation, 91. 

Glass, contraction of, 124; absorption 
by, 153; transparency of, 152; un- 
annealed, 124. 

Graduation of thermometer, 9—12. 

Graham’s Mercurial pendulum, 67; 
law of diffusion, 86. 

Gravitation units, 181. 

Gravity, variation of, 8. 

Gridiron pendulum, 67. 

Hail, 175. 

Halo, 175. 

Harrison’s gridiron pendulum, 67. 

Heat, a quantity, 21—24; amounts 
of, 23; conduction of, 131—143; 
convection of, 131, 143—146; en¬ 
gines, .193 et seq.; mechanical 

16 


G. 


242 


INDEX. 


equivalent of, 190 et seq.; nature 
of, 185; of mixtures, 23; sensation 
of, 1—3; sources of, 37—47; trans¬ 
mission of, 3,131,132; unit of, 24. 

Heights, measurement of, by water 
boiling, 98. 

Hero’s engine, 118. 

Hoar-frost, 176. 

Homogeneous solids, Thermal con¬ 
ductivity of, 140. 

Hope’s experiment on maximum 
density of water, 60. 

Horse power, 181; of engine, 215. 

Humidity, degree of, 104. 

Hygrometer’s, Daniell’s, 103; Dine’s, 
103; wet and dry bulb, 104. 

Hygrometry, 104—107. 

Hypsometer, 8, 98. 

Ice, calorimeter, 31—34; changes in 
when heated, 121; evaporation of, 
120; expansion of, 60,88; fusion 
of, 30; latent heat of fusion of, 
108; regelation of, 91; specific 
heat of, 35. 

Incandescent lamps, 127. 

Indiarubber, contraction of, 43, 123. 

Indicator, Watt’s, 208; Richards’, 
210; Dark’s, 210. 

Indicator diagram, explained, 204 
et seq.; normal diagram of high- 
pressure engine, 212; calculation 
of work done and horse-power 
from, 215; diagrams of pumping 
engine, 219; diagrams of engine 
with variable load, 220. 

Inversion, thermo-electric, 128. 

Iodine, sublimation of, 120. 

Isentropic lines, 208. 

Isothermal lines, 205; of air, 205; of 
vapour and liquid, 206; of Car¬ 
bonic anhydride, 206. 

Jolly, Professor, air thermometer, 77; 
mirror scale, 72. 

Joule, heating effect of electric cur¬ 
rent through wire, 44, 192; on the 
expansion of air, 82, 180, 181; 
mechanical equivalent of heat, 
190—192, 194; temperature of 
water at maximum density, 135; 
unit of work, 182. 

Kinetic energy, 179; conversion of, 
into Potential energy, 180. 


Lamp, safety, 142. 

Lampblack, radiation from, 159. 

Latent heat, 87, 88, 108; objection 
to term, 88; of fusion, 30, 87; of 
evaporation, 108; of fusion of ice, 
87; of steam at different tem¬ 
peratures, 109; method of measur¬ 
ing, 110; nature of, 45. 

Lavoisier’s and Laplace’s calorimeter, 
31; measurement of expansion, 50. 

Leidenfrost’s phenomenon, 118. 

Length, standard of, 92. 

Leslie’s cube, 159; differential ther¬ 
mometer, 81. 

Light, its nature, 150; identical with 
radiant heat, 150. 

Linear expansion, 50—53; measure¬ 
ment of, 51; table of coefficients 
of, 53. 

Liquefaction of gases, 111; Andrews’ 
apparatus for, 112; Cailletet’s ap¬ 
paratus for, 113; table of, 111. 

Liquefaction, latent heat of, 30, 87. 

Liquids, convection of heat by, 143; 
defined, 49; expansion of, 51, 52; 
methods of measuring apparent 
expansion of, 55—58; specific heat 
of, 33, 35. 

Magnetism, effect of heat on, 125. 

Manometer, 101. 

Marriotte’s law of expansion of gases, 
71; tube, 71. 

Mason’s wet and dry bulb hygrome¬ 
ter, 104. 

Matthiessen’s method of measuring 
expansion, 59; table of expansion 
of water, 61. 

Maximum pressure of vapour, 100; 
thermometer, 18. 

Mayer, on the mechanical equivalent 
of heat, 301. 

Measurement of vapour pressure, 101. 

Measurers of time, effect of tempera¬ 
ture on, 66. 

Mechanical equivalent of heat, 189 
et seq. 

Mechanical properties of bodies, 
effects of heat on, 123; energy con¬ 
verted into heat, 42—44. 

Melloni, on radiation transmitted by 
substances, 154. 

Melting points, effects of pressure 
on, 89, 90; liquids cooled below 
without solidification, 91. 



INDEX. 


245 


Mercurial pendulum, 67; thermome¬ 
ter, see Thermometer. 

Mercury, absolute expansion of, 57, 
58; apparent expansion of, 55, 
56; freezing of, in a red-hot vessel, 
119. 

Metallic thermometer, Breguet’s, 69. 

Metals, expansion of, 50—53, 60, 
70; thermal conductivity of, 134 
et seq.; thermo-electric arrange¬ 
ment of, 128. 

Mirror scale, Professor Jolly’s, 72. 

Mixture, freezing, 112; method of 
measuring specific heats by, 26— 
30. 

Moisture in air, determination of, 
104. 

Molecular theory of gases, 49, 78, 
86, 106. 

Mont Blanc, boiling point on, 102. 

Natterer, cold produced by, 112. 

Newton’s law of cooling, 161; state¬ 
ment of the Principle of the con¬ 
servation of energy, 182. 

Norwegian cooking pot, 134. 

Oxygen, coefficient of expansion of, 
73 ; heat produced by combustion 
in, 38; liquefaction of, 111. 

Page and Dupre on specific heat of 
alcohol and water, 109. 

Papin’s digester, 102. 

Peltier’s effect, 127. 

Pendulum, compensating, 66—68; 
Ellicott’s, 67; Graham’s, 67; Har¬ 
rison’s, 67; zinc-iron, 67. 

Petit and Dulong’s experiments on 
cooling, 161; measurement of ab¬ 
solute expansion of liquids, 57. 

Phillip’s maximum thermometer, 18. 

Pictet’s liquefaction of gases, 111, 
114. 

Platinum, specific heat of, 34; wire 
used as an electric pyrometer, 
126 ; wire heated by an electric 
current, 126. 

Polarization of radiation from tour¬ 
maline, 166. 

Potential energy, 179. 

Poundal, 181. 

Power, 181. 

Pressure, critical, 116; ebullition 
under diminished, 99, 117; effect 


of, on boiling point, 97, 98, 102; 
effect of, on melting point, 89, 90; 
maximum of vapours, 93, 100; of 
aqueous vapour, 95, 120; of gases, 
50, 79; of gases, relation between 
volume and, 71; of gases, relation 
between temperature, volume and, 
71, 77; of vapour, dependent on 
temperature, 96 et seq.; of vapour, 
with air present, 100; of mixed 
vapours, 95; reduction of, effect 
on boiling point, 99; specific heats 
of gases at constant, 82; standard 
atmospheric, 8. 

Prevost’s theory of exchanges, 162 
et seq. 

Prince Bupert’s drops, 124. 

Psychrometer, 104. 

Pyrometer, Begnault’s mercury, 83; 
the electric or Siemens’, 85, 126; 
Wedgwood’s, 85. 

Quality, distinction between quan¬ 
tity and, 22. 

Quantity, heat a physical, 21, 22. 

Badiation, 131, 147, 148; analysis 
of, 148; definition of, 131; trans¬ 
mission of, 154; from tourmaline, 
polarised, 166; laws of intensity 
and propagation, 157, 158; relation 
between, and absorption, 152, 164; 
repulsion produced by, 167; table 
of relative powers of different sub¬ 
stances for transmitting, 152. 

Badiant energy, 147—152; absorp¬ 
tion of, 152 ; double refraction of, 
155; effects of, 38; nature of, 37, 
38, 148—152; passage of, through 
ice, 156; polarization of, 156, 
166; propagation of, 157 ; reflec¬ 
tion of, 150; refraction of, 155; 
repulsion produced by, 167. 

Badiant heat, see Badiant energy. 

Badiators, good and bad, 159. 

Badiometer, Cooke’s, 168; Schus¬ 
ter’s experiments on, 170; theory 
of, 169. 

Bailway, expansion of iron rods on, 
70. 

Beaumur’s thermometric scale, 11. 

Beduction of different thermometric 
scales, 13. 

Beflection, apparent of cold, 161; of 
heat, 151; of heat, laws of, 152. 


244 


INDEX. 


Reflectors and radiators, 159. 

Refraction of heat, laws of, 155; 
double, 156. 

Regelation, 89—91. 

Regnault’s calorimeter for liquids, 
34; comparison of mercurial and 
air thermometers, 83 ; determina¬ 
tion of maximum pressure of aque¬ 
ous vapour, 83, 105 ; latent heat of 
steam, 108; measurement of spe¬ 
cific heat of air at constant pres¬ 
sure, 33, 82; mercury pyrometer, 
83; on aqueous vapour above the 
dew-point, 105; on evaporation, 92; 
on pressure of aqueous vapour, 95, 
120; rate of increase of pressure 
of gases, 79; table of coefficients 
of expansion of gases, 79. 

Regnault’s dew-point instruments, 
104. 

Repulsion produced by radiation, 
167. 

Resistance, electrical, effect of heat 
upon, 125; heat produced by, 43, 
125. 

Reversible engines, 197. 

Reynolds’, Prof. O., theory of the 
radiometer, 169. 

Rigidity of solids, 48. 

Rock salt, diathermancy of, 152. 

Rumford, Count, on the nature of 
heat, 186 et seq. ; on generation 
of heat by friction, 186. 

Rupert’s drops, 124. 

Rutherford’s maximum thermome¬ 
ter, 18; minimum thermometer, 
18. 

Safety lamps, 142. 

Salts, effect on boiling point of dis¬ 
solved, 10, 97; heat developed by 
crystallization of, 45, 91. 

Saturation, 45, 102, 106. 

Schuster’s, Dr, experiment with the 
radiometer, 170. 

Seguin on the mechanical equivalent 
of heat, 189. 

Selective absorption, 152—155. 

Senarmont, Dr, on conduction in 
crystals, 140. 

Siemen’s furnace, 39; pyrometer, 
85. 

Singing of kettle, 97. 

Six’s self-registering thermometer, 


Snow, 90, 175; carbonic anhydride, 
111; direct evaporation of, 92. 

Sodium vapour, radiation from, 152. 

Solidification, 88, 111. 

Solids, conduction of heat in homo¬ 
geneous, 140; definition of, 48; 
expansion of, 62; specific heat of, 
34 ; rigidity of, 48. 

Solutions supersaturated, 45. 

Sources of heat, 37—47. 

Specific gravity bottle, 56, 57. 

Specific heat, 25, 28, 82; depend¬ 
ence on external conditions, 36; 
effect of temperature on, 35; 
measurement of, 28; of gas, at 
constant pressure, 33, 82, 83; of 
gas, at constant volume, 83, 195; 
of gas, comparison between at 
constant pressure and volume, 
81, 83,195 ; of substances in differ¬ 
ent states compared, 34, 35; of 
water, 108; of water, at different 
temperatures, 25; of saturated 
steam, 201; table of, 34. 

Spectrum of heated bodies, 150, 151; 
reversal of spectrum, 152. 

Spheroidal state, 48, 117; forms as¬ 
sumed by water in, 119. 

Standard of length, 65. 

State, change of, 37, 45, 46, 87; re¬ 
duction to liquid, 87; spheroidal, 
117; of strain, 48. 

Steam, bubbles of, 98; latent heat 
of, 109, 110, 111; maximum pres¬ 
sure of, 105; saturated, 102; 
specific heat of, 35; specific heat 
of saturated, 201; temperature of, 
constant, 10; superheated, 202. 

Stewart Balfour, measurement of 
hygrometric state, 106; on pressure 
and temperature of air, 76. 

Strains produced by contraction, 64, 
124. 

Sublimation, 92, 120. 

Sulphur, forms of, 46. 

Sun, radiation from, 38; source of 
energy, 46. 

Super-heated vapour, 105. 

Surface tension, 49. 

Surfaces, absorption and radiation 
of, 158, 159. 

Table of comparison of mercurial 
and air thermometers, 83; con¬ 
ditions of liquefaction of gases. 


INDEX. 


245 


112; coefficients of linear expan¬ 
sion, 53; critical pressure and tem¬ 
perature, 116 ; expansion of gases, 
79 ; expansion of water, 61; heat 
developed by different fuels, 41 ; 
maximum pressure of aqueous 
vapour, 105; percentage radiation 
transmitted by different substan¬ 
ces, 154 ; rate of increase of pres¬ 
sure of different gases, 79; specific^ 
heats, 34, 35; thermal conduc¬ 
tivities, 142; thermo-electric ar¬ 
rangement of metals, 128. 

Tait, Professor, on thermo-electric 
combinations, 129. 

Temperature, absolute, 76, 197 ; de¬ 
finition of, 2; effect on bodies, 
123—126 ; effect on electrical pro¬ 
perties of bodies, 126; effect on 
magnetism, 126; effect on me¬ 
chanical properties of bodies, 123, 
124; effect on radiation, 161; effect 
on specific heat, 35; effect on elec¬ 
trical conductivity, 126; effect on 
time measures, 66; equilibrium 
of, 4; instruments for measuring, 
4, 129; measurement of, 4, 5, 129; 
necessary for combustion, 40; of 
gases, relation between pressure, 
volume and, 77; primitive notion 
of, 2. 

Tempering of steel, 123, 124. 

Tension of surfaces, 49. 

Thermal conductivity, definition of, 
137; conductivities, comparison 
of, 134—136, 140—142 ; measure 
of, 137, 138; Principal Forbes’ 
experiments on, 139; table of, 
140; equilibrium, 3. 

Thermo-electric currents, 127, 128; 
inversion, 129; order of metals, 
128; piles, 130; Thomson effect, 129. 

Thermometer, air, 76, 80; advan¬ 
tages of fluids for, 5; Breguet’s 
metallic, 69; definition of, 4; dif¬ 
ferential, 80; liquids other than 
mercury used for, 16; Maximum, 
18—20; Maximum and mini¬ 
mum combined, 19; Mercurial, 
advantages of, 17; calibration of, 
12; causes of error, 10—12; com¬ 
parison of, with air thermometer, 
17, 73, 83; construction of, 7; 
determination of boiling point on, 

9,10,99 ; determination of freezing 


point on, 9; graduation of, 11; 
liow filled, 7; Minimum, 18, 19; 
natural standard, 13 ; open range, 
13; scale, Sir W. Thomson’s abso¬ 
lute, 197; sensitive, 13 > position 
of, when used, 10; weight, 20; wet 
and dry bulb, 104. 

Thermometric scales, 6, 11, 13—17; 

. indicated by different substances, 
16; rules for conversion of, 13, 14. 

Thermopiles, 130. 

Thilprier’s apparatus, 111. 

Thompson’s Calorimeter, 40. 

Thomson effect, 129. 

Thomson, Professor James, on the 
lowering of the freezing point by 
pressure, 89. 

Time measurers, 66. 

Torsion, heat generated by work 
against, 43. 

Tourmaline, polarizes dark radia¬ 
tion, 154. 

Transformation of energy, 132. 

Transmission of heat, 131, 132, 152. 

Triple point, 121. 

Tyndall, on relative absorbing powers 
of gases, 155. 

Uncrystallized solids, expansion of, 
54. 

Undulatory motion of ether consti¬ 
tutes radiant energy, 150. 

Unit, of force, 176, 181; heat, 24; 
length, 65, 181; mass, 181; time, 
181; work, 181. 

Units, absolute, 181, 182; C.G.S., 
182; gravitation, 182. 

Vacua, action of gases as, 93, 101. 

Vaporisation, cold produced by, 111, 
133; effect of chemical affinity on, 
112; latent heat of, 110; in air, 
101; in vacuo, 93. 

Vapour, aqueous, application of mole¬ 
cular theory to, 107; table of max¬ 
imum pressure, 105; condensation 
of, 102; definition of, 92; density 
of, 99; pressure of, 93—100; in 
presence of air, 100; measurement 
of, 101—105; saturated, definition 
of 102 ; super-heated, 105. 

Vapours, pressure of mixed, 95; dis¬ 
tinction between vapours and 
gases, 92. 

Vibration in a spheroid, 119, 120. 


246 


INDEX. 


Viscosity, 49. 

Volatile, body, definition of, 92. 

Voltaic electricity, heating effect of, 
37, 44, 126. 

Volume, critical, 116; of bodies, effect 
of heat on, 50; of gas, method of 
finding for different temperatures, 
75. 

Volume of gas, relation between pres¬ 
sure, temperature and, 77. 

Wall, flow of heat, across a, 137. 

Water, action of heat upon, 60; ex¬ 
pansion of, 61, 62; forms assum¬ 
ed by in spheroidal state, 119; gas, 
92; high specific heat of, 108; 
latent heat of, 108; maximum 
density of, 59, 145; specific heat 
of, at different temperatures, 25; 
super-heating of, 98; volume of, at 
different temperatures, 60. 

Watt, James, on latent heat of 
vaporisation, 108; indicator, 210, 


Watt, unit of power, 182. 

Wedgwood’s pyrometer, 85. 

Weight thermometer, 20, 56, 59, 60, 
61. 

Wells, Dr, on the formation of dew, 
176, 

Wet and dry bulb hygrometer, 104. 

Wiedemann and Franz on conduc¬ 
tivity, 141. 

Winds, Trade and counter Trade, 172. 

Wire-drawing, 213. 

Wollaston’s cryophorus, 96. 

Work, done by perfect engines, 196; 
heat equivalent of, 192; measure 
of, 177; transformed into heat, 
187, 189, 191. 

Yard, imperial standard, 65. 

Zero, absolute, 74; change of in 
thermometers, 9; of thermometric 
scales, 11. 


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is. 

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14 


George Bell and Sons' 


Practical Guide to Modem French Conversation. 15th Thou¬ 

sand. Fcap. 8vo. 2s. 6d. 

French Poetry for the Young. With Notes. 4th Edition. Fcap. 

8 vo. 2s. 

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Modem French-English and English-French Dictionary. 3rd 

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GOMBERT’S FRENCH DRAMA. 


Being a Selection of the best Tragedies and Comedies of Moli&re, 
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Moliere Le Misanthrope. L’Avare. Le Bourgeois Gentilhomme. Le 
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Maris. Le Mddecin malgr^ Lui. 


Racine: —Ph4dre. Esther. Athalie. Iphig&iie. Les Plaideurs. La 
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P. Corneille :—Le Cid. Horace. Cinna. Polyeucte. 


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GERMAN SCHOOL CLASSICS. 

Meister Martin, der Kiifner. Erzahlung von E. T. A. Hoffman. 
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The Elements of the English Language. By E. Adams, Ph.D. 

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Educational Works. 


15 


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Luther. By Sarah Crompton. Is. 








16 George Bell and Sons 9 Educational Works. 


BOOKS FOR YOUNG READERS. 

A Series of Reading Books designed to facilitate the acquisition of the •power 
of Reading by very young Children. In 9 vols. limp cloth, 6 d. each. 

Tot and the Cat. A Bit of Cake. The Jay. The N 
Black Hen’s Nest. Tom and Ned. Mrs. Bee. 

The Cat and the Hen. Sam and his Dog Red-leg. 

Bob and Tom Lee. A Wreck. 

The New-born Lamb. The Rosewood Box. Poor 

Fan. Sheep Dog. 

The Story of Three Monkeys. 

Story of a Cat. Told by Herself. 

The Blind Boy. The Mute Girl. A New Tale of 

Babes in a Wood. 

The Dey and the Knight. The New Bank Note. 

The Royal Visit. A King’s Walk on a Winter’s Day. 

Queen Bee and Busy Bee. 

Gull’s Crag. 

A First Book of Geography. By the Rev. C. A. Johns. 

Illustrated. Double size. Is. 


Suitable 

for 

Infants. 


Suitable 

for 

Standards 

I. & II. 


BELL’S READING-BOOKS. 


FOR SCHOOLS AND PAROCHIAL LIBRARIES. 

The popularity of the * Books for Young Readers ’ is a sufficient proof that 
teachers and pupils alike approve of the use of interesting stories, in place of 
the dry combination of letters and syllables, of which elementary reading-books 
generally consist. The Publishers have therefore thought it advisable to extend 
the application of this principle to books adapted for more advanced readers. 

Now Ready. Post 8 vo. Strongly bound in cloth , Is. each. 

Grimm’s German Tales. (Selected.) 

Andersen’s Danish Tales. Illustrated. (Selected.) ) Suitable 
Great Englishmen. Short Lives for Young Children. ( , 

Great Englishwomen. Short Lives of. f 

Masterman Ready. ByCapt. Marryat. Illus. (Abgd.) J 


Friends in Fur and Feathers. By Gwynfryn. 

Parables from Nature. (Selected.) By Mrs. Gatty. 
Lamb’s Tales from Shakespeare. (Selected.) 
Edgeworth’s Tales. (A Selection.) \ 

Gulliver’s Travels. (Abridged.) 

Robinson Crusoe. Illustrated. 

Arabian Nights. (A Selection Rewritten.) 

Gatty’s Light of Truth. 

The Vicar of Wakefield. ' 

Settlers in Canada. By Capt. Marryat. (Abridged.) 
Marie: Glimpses of Life in France. By A. R. Ellis. 
Poetry for Boys. Selected by D. Munro. 

Southey’s Life of Nelson. (Abridged.) ) 

Life of the Duke ofWellington, with Maps and Plans. 

Sir Roger de Coverley and other Essays from the 

Spectator. * 

The Romance of the Coast. By J. Runciman. 

Others in preparation. < 


Standards 

IV. & F. 


Standards 
v. vi. ci¬ 
vil. 


London : Printed by Strangeways & Sons, Tower Street, St. Martin’s Lane. 











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